around 300 equation tests
<math xmlns="http://www.w3.org/1998/Math/MathML"> <mtable> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mn>2</mn> <mo>⁢</mo> <mrow> <mo form="prefix" largeop="false" stretchy="false" lspace="0.166667em" rspace="0em">∑</mo> <mrow> <mi>a</mi> <mo>⁢</mo> <mi>b</mi> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <msup> <mi>x</mi> <mrow> <mo form="postfix" lspace="0em" rspace="0.000000em">′</mo> <mn>3</mn> </mrow> </msup> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mrow> <msup> <mi>f</mi> <mo form="postfix">′</mo> </msup> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi>x</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi mathcolor="gray">cos</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>1</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi>z</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <munderover> <mo form="prefix" movablelimits="false" largeop="false" stretchy="true" maxsize="1.4" minsize="1.4" lspace="0.277778em" rspace="0em">∑</mo> <mrow> <mi>n</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>0</mn> </mrow> <mi>∞</mi> </munderover> <mrow> <msub> <mi>a</mi> <mi>n</mi> </msub> <mo>⁢</mo> <msup> <mi>z</mi> <mi>n</mi> </msup> </mrow> </mrow> </mrow> <mtext mathcolor="black">, </mtext> <mrow> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">|</mo> <mi>z</mi> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">|</mo> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em"><</mo> <mi>R</mi> </mrow> <mo>​</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>R</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">≠</mo> <mn>0</mn> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow id="one"> <mrow> <msub> <mo form="prefix" largeop="false" stretchy="true" maxsize="1.4" minsize="1.4" rspace="0em">∫</mo> <mi>C</mi> </msub> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <munderover> <mo form="prefix" movablelimits="false" largeop="false" stretchy="true" maxsize="1.4" minsize="1.4" rspace="0em">∑</mo> <mrow> <mi>n</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>0</mn> </mrow> <mi>∞</mi> </munderover> <mrow> <msub> <mi>a</mi> <mi>n</mi> </msub> <mo>⁢</mo> <msup> <mi>z</mi> <mi>n</mi> </msup> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.166667em" rspace="0em">ⅆ</mo> <mi>z</mi> </mrow> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <munderover> <mo form="prefix" movablelimits="false" largeop="false" stretchy="true" maxsize="1.4" minsize="1.4" lspace="0.277778em" rspace="0em">∑</mo> <mrow> <mi>n</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>0</mn> </mrow> <mi>∞</mi> </munderover> <mrow> <msub> <mi>a</mi> <mi>n</mi> </msub> <mo>⁢</mo> <mrow> <msub> <mo form="prefix" largeop="false" stretchy="true" maxsize="1.4" minsize="1.4" lspace="0.166667em" rspace="0em">∫</mo> <mi>C</mi> </msub> <mrow> <msup> <mi>z</mi> <mi>n</mi> </msup> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.000000em" rspace="0em">ⅆ</mo> <mi>z</mi> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow id="two"> <mrow> <munder> <mo mathcolor="gray" form="prefix" movablelimits="false" rspace="0.166667em">lim</mo> <mrow> <mi>n</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">→</mo> <mi>∞</mi> </mrow> </munder> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">|</mo> <mrow> <msub> <mo form="prefix" largeop="false" stretchy="true" maxsize="1.4" minsize="1.4" rspace="0em">∫</mo> <mi>C</mi> </msub> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">[</mo> <mrow> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi>z</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <munderover> <mo form="prefix" movablelimits="false" largeop="false" stretchy="true" maxsize="1.4" minsize="1.4" lspace="0.222222em" rspace="0em">∑</mo> <mrow> <mi>k</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>0</mn> </mrow> <mi>n</mi> </munderover> <mrow> <msub> <mi>a</mi> <mi>k</mi> </msub> <mo>⁢</mo> <msup> <mi>z</mi> <mi>k</mi> </msup> </mrow> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">]</mo> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.166667em" rspace="0em">ⅆ</mo> <mi>z</mi> </mrow> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">|</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>0</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>n</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">≥</mo> <mrow> <mi>N</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi>ε</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">⇒</mo> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">|</mo> <mrow> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi>z</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <munderover> <mo form="prefix" movablelimits="false" largeop="false" stretchy="true" maxsize="1.4" minsize="1.4" lspace="0.222222em" rspace="0em">∑</mo> <mrow> <mi>k</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>0</mn> </mrow> <mi>n</mi> </munderover> <mrow> <msub> <mi>a</mi> <mi>k</mi> </msub> <mo>⁢</mo> <msup> <mi>z</mi> <mi>k</mi> </msup> </mrow> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">|</mo> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em"><</mo> <mi>ε</mi> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mn>10</mn> <mtext mathcolor="green"> Bq</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> Ci</mtext> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mn>10</mn> <mtext mathcolor="green"> amol</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> Emol</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> fmol</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> Gmol</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> kmol</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> Mmol</mtext> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mn>10</mn> <mtext mathcolor="green"> μmol</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> mmol</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> mol</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> nmol</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> Pmol</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> pmol</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> Tmol</mtext> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mn>10</mn> <mtext mathcolor="green"> acre</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> hectare</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mstyle mathcolor="green"> <msup> <mtext> ft</mtext> <mn>2</mn> </msup> </mstyle> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mstyle mathcolor="green"> <msup> <mtext> in</mtext> <mn>2</mn> </msup> </mstyle> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mstyle mathcolor="green"> <msup> <mtext> m</mtext> <mn>2</mn> </msup> </mstyle> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mn>10</mn> <mtext mathcolor="green"> A</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> kA</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> μA</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> mA</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> nA</mtext> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mn>10</mn> <mtext mathcolor="green"> F</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> μF</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> mF</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> nF</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> pF</mtext> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mn>10</mn> <mtext mathcolor="green"> C</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>1.0</mn> <mtext mathcolor="green"> m/s/s</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>0.1</mn> <mstyle mathcolor="green"> <mrow> <mtext> m</mtext> <mo>/</mo> <mstyle mathcolor="green"> <msup> <mtext>s</mtext> <mn>2</mn> </msup> </mstyle> </mrow> </mstyle> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mn>10</mn> <mtext mathcolor="green"> kS</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> μS</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> mS</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> S</mtext> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mn>10</mn> <mtext mathcolor="green"> kV</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> MV</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> μV</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> mV</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> nV</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> pV</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> V</mtext> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mn>10</mn> <mtext mathcolor="green"> GΩ</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> kΩ</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> MΩ</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> mΩ</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> Ω</mtext> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mn>10</mn> <mtext mathcolor="green"> Btu</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> cal</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> eV</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> erg</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> GeV</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> GJ</mtext> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mn>10</mn> <mtext mathcolor="green"> J</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> kcal</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> kJ</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> MeV</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> MJ</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> μJ</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> mJ</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> nJ</mtext> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mn>10</mn> <mtext mathcolor="green"> dyn</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> kN</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> MN</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> μN</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> mN</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> N</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> ozf</mtext> </mrow> <mo form="infix" 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mathbackground="transparent"> <mrow> <mrow> <mn>10</mn> <mtext mathcolor="green"> ml</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> pint</mtext> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>10</mn> <mtext mathcolor="green"> qt</mtext> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mfrac> <mn>1</mn> <mrow> <mi>x</mi> <mo rspace="0.000000em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mi>y</mi> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mfrac> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mrow> <mo form="prefix" largeop="false" stretchy="false" lspace="0.222222em" rspace="0em">∫</mo> <mrow> <msup> <mi>e</mi> <mrow> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo>⁢</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> </mrow> </msup> <mo>⁢</mo> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>y</mi> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.000000em" rspace="0em">ⅆ</mo> <mi>y</mi> </mrow> </mrow> </mrow> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <msub> <mi>C</mi> <mn>1</mn> </msub> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mo>⁢</mo> <msup> <mi>e</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>⁢</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> </mrow> </msup> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mrow> <msub> <mo form="prefix" rspace="0em">ⅅ</mo> <mi>x</mi> </msub> <mi>y</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mi>y</mi> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>x</mi> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em">(</mo> <mfrac linethickness="0px"> <mn>1</mn> <mn>2</mn> </mfrac> <mo form="postfix" fence="true" stretchy="true" lspace="0em" rspace="0em">)</mo> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em">(</mo> <mrow> <mstyle displaystyle="false" scriptlevel="0"> <mfrac linethickness="0px"> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo form="postfix" fence="true" stretchy="true" lspace="0em" rspace="0em">)</mo> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em">(</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac linethickness="0px"> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo form="postfix" fence="true" stretchy="true" lspace="0em" rspace="0em">)</mo> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em">[</mo> <mfrac linethickness="0px"> <mn>1</mn> <mn>2</mn> </mfrac> <mo form="postfix" fence="true" stretchy="true" lspace="0em" rspace="0em">]</mo> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em">(</mo> <mrow> <mstyle displaystyle="false" scriptlevel="0"> <mfrac linethickness="0px"> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo form="postfix" fence="true" stretchy="true" lspace="0em" rspace="0em">)</mo> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em">{</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac linethickness="0px"> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo form="postfix" fence="true" stretchy="true" lspace="0em" rspace="0em">}</mo> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em">〈</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo form="postfix" fence="true" stretchy="true" lspace="0em" rspace="0em">〉</mo> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em">⌊</mo> <mrow> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo form="postfix" fence="true" stretchy="true" lspace="0em" rspace="0em">⌋</mo> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em">⌈</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo form="postfix" fence="true" stretchy="true" lspace="0em" rspace="0em">⌉</mo> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em">↑</mo> <mfrac linethickness="1pt"> <mn>1</mn> <mn>2</mn> </mfrac> <mo form="postfix" fence="true" stretchy="true" lspace="0em" rspace="0em">↑</mo> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em">↓</mo> <mrow> <mstyle displaystyle="false" scriptlevel="0"> <mfrac linethickness="1pt"> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo form="postfix" fence="true" stretchy="true" lspace="0em" rspace="0em">↓</mo> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em">↕</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac linethickness="1pt"> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo form="postfix" fence="true" stretchy="true" lspace="0em" rspace="0em">↕</mo> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>⁢</mo> <mrow> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo>⁢</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mfrac linethickness="1pt"> <mn>1</mn> <mn>2</mn> </mfrac> <mo>⁢</mo> <mrow> <mstyle displaystyle="false" scriptlevel="0"> <mfrac linethickness="1pt"> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo>⁢</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac linethickness="1pt"> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mfrac linethickness="0px"> <mn>1</mn> <mn>2</mn> </mfrac> <mo>⁢</mo> <mrow> <mstyle displaystyle="false" scriptlevel="0"> <mfrac linethickness="0px"> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo>⁢</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac linethickness="0px"> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>a</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mi>b</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mi>b</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mi>a</mi> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>2</mn> <mn>5</mn> </mfrac> </mstyle> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>3</mn> <mn>7</mn> </mfrac> </mstyle> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <mrow> <mn>2</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">⋅</mo> <mn>7</mn> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>3</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">⋅</mo> <mn>5</mn> </mrow> </mrow> <mn>35</mn> </mfrac> </mstyle> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>29</mn> <mn>35</mn> </mfrac> </mstyle> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">|</mo> <mi>a</mi> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">|</mo> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">{</mo> <mtable align="axis" columnalign="right left left"> <mtr> <mtd> <mi>a</mi> </mtd> <mtd> <mtext mathcolor="black">if</mtext> </mtd> <mtd> <mrow> <mi>a</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">≥</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mi>a</mi> </mrow> </mtd> <mtd> <mtext mathcolor="black">if</mtext> </mtd> <mtd> <mrow> <mi>a</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em"><</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace"/> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <msup> <mi>a</mi> <mi>n</mi> </msup> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <munder> <munder> <mrow> <mi>a</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">⋅</mo> <mi>a</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">⋅</mo> <mi>⋯</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">⋅</mo> <mi>a</mi> </mrow> <mo stretchy="true">︸</mo> </munder> <mrow> <mi>n</mi> <mtext mathcolor="black"> factors</mtext> </mrow> </munder> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <msup> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mi>a</mi> <mi>b</mi> </mfrac> </mstyle> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mi>n</mi> </mrow> </msup> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <msup> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mi>b</mi> <mi>a</mi> </mfrac> </mstyle> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mi>n</mi> </msup> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mroot> <mi>a</mi> <mi>n</mi> </mroot> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mi>b</mi> </mrow> <mtext mathcolor="black">  means </mtext> <mrow> <msup> <mi>b</mi> <mi>n</mi> </msup> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mi>a</mi> </mrow> <mtext>.</mtext> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mroot> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>16</mn> <mn>81</mn> </mfrac> </mstyle> </mrow> <mn>4</mn> </mroot> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mroot> <mn>16</mn> <mn>4</mn> </mroot> <mroot> <mn>81</mn> <mn>4</mn> </mroot> </mfrac> </mstyle> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> </mstyle> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">{</mo> <mrow> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">∣</mo> <mrow> <mrow> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">≠</mo> <mn>0</mn> </mrow> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mrow> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">≠</mo> <mn>1</mn> </mrow> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">}</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <msub> <mi>a</mi> <mi>n</mi> </msub> <mo>⁢</mo> <msup> <mi>x</mi> <mi>n</mi> </msup> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <msub> <mi>a</mi> <mrow> <mi>n</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>1</mn> </mrow> </msub> <mo>⁢</mo> <msup> <mi>x</mi> <mrow> <mi>n</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>1</mn> </mrow> </msup> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>⋯</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>⁢</mo> <mi>x</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <msup> <mi>a</mi> <mn>3</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <msup> <mi>b</mi> <mn>3</mn> </msup> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mi>a</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mi>b</mi> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <msup> <mi>a</mi> <mn>2</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mi>a</mi> <mo>⁢</mo> <mi>b</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <msup> <mi>b</mi> <mn>2</mn> </msup> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <msup> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>x</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>y</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>H</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">{</mo> <mrow> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mtable align="axis"> <mtr> <mtd> <mi>a</mi> </mtd> <mtd> <mi>b</mi> </mtd> </mtr> <mtr> <mtd> <mi>c</mi> </mtd> <mtd> <mi>d</mi> </mtd> </mtr> </mtable> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">∈</mo> <mi>G</mi> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">∣</mo> <mrow> <mrow> <mrow> <mi>a</mi> <mo>⁢</mo> <mi>d</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mi>b</mi> <mo>⁢</mo> <mi>c</mi> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>1</mn> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">}</mo> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="false">|</mo> <mi>x</mi> <mo form="postfix" fence="true" stretchy="false">|</mo> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">||</mo> <mi>y</mi> <mo form="postfix" fence="true" stretchy="false">||</mo> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">{</mo> <mi>z</mi> <mo form="postfix" fence="true" stretchy="false">}</mo> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">[</mo> <mrow> <mi>a</mi> <mo>⁢</mo> <mi>c</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">]</mo> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi>b</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">[</mo> <mrow> <mi>a</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>b</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">]</mo> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.055556em">=</mo> <mn>1</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>1</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.388889em">=</mo> <mn>1</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.500000em">=</mo> <mn>1</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">[</mo> <mrow> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mfrac> <mn>10</mn> <mn>3</mn> </mfrac> </mrow> <mo form="infix" lspace="0.166667em" rspace="0.222222em">,</mo> <mrow> <mo form="prefix" lspace="0.222222em" rspace="0em">−</mo> <mfrac> <mn>7</mn> <mn>3</mn> </mfrac> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">∪</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mfrac> <mn>7</mn> <mn>3</mn> </mfrac> </mrow> <mo form="infix" lspace="0.166667em" rspace="0.222222em">,</mo> <mrow> <mo form="prefix" lspace="0.222222em" rspace="0em">−</mo> <mfrac> <mn>4</mn> <mn>3</mn> </mfrac> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">]</mo> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mrow> <mi>A</mi> <mo>⁢</mo> <mfrac> <mrow> <mo form="prefix" rspace="0em">∂</mo> <mi>u</mi> </mrow> <mrow> <mo form="prefix" rspace="0em">∂</mo> <mi>x</mi> </mrow> </mfrac> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mi>B</mi> <mo>⁢</mo> <mfrac> <mrow> <mo form="prefix" rspace="0em">∂</mo> <mi>u</mi> </mrow> <mrow> <mo form="prefix" rspace="0em">∂</mo> <mi>y</mi> </mrow> </mfrac> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mi>C</mi> <mo>⁢</mo> <mi>u</mi> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mi>E</mi> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <munderover> <mo form="prefix" movablelimits="true" largeop="false" stretchy="false" rspace="0em">∑</mo> <mtext>​</mtext> <mtext>​</mtext> </munderover> <mi>x</mi> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <munderover> <mo form="prefix" movablelimits="true" largeop="false" stretchy="false" rspace="0em">∑</mo> <mtable rowspacing="0px" columnspacing="0px"> <mtr> <mtd> <mrow> <mn>1</mn> <mo form="infix" lspace="0.277778em" rspace="0.277778em"><</mo> <mi>i</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em"><</mo> <mn>10</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>1</mn> <mo form="infix" lspace="0.277778em" rspace="0.277778em"><</mo> <mi>j</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em"><</mo> <mn>10</mn> </mrow> </mtd> </mtr> </mtable> <mtext>​</mtext> </munderover> <msup> <mn>2</mn> <mrow> <mi>i</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">+</mo> <mi>j</mi> </mrow> </msup> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <msubsup> <mi>Γ</mi> <msubsup> <mn>1</mn> <msup> <mspace width="veryverythinmathspace"/> <mtable rowspacing="0px" columnspacing="0px"> <mtr> <mtd> <msubsup> <mn>2</mn> <msup> <mspace width="veryverythinmathspace"/> <mtable rowspacing="0px" columnspacing="0px"> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> <mtr> <mtd> <mn>4</mn> </mtd> </mtr> </mtable> </msup> <mtext>​</mtext> </msubsup> </mtd> </mtr> <mtr> <mtd> <msubsup> <mn>5</mn> <msup> <mspace width="veryverythinmathspace"/> <mtable rowspacing="0px" columnspacing="0px"> <mtr> <mtd> <mn>6</mn> </mtd> </mtr> <mtr> <mtd> <mn>7</mn> </mtd> </mtr> </mtable> </msup> <mtext>​</mtext> </msubsup> </mtd> </mtr> </mtable> </msup> <mtext>​</mtext> </msubsup> <msup> <mn>1</mn> <mtable rowspacing="0px" columnspacing="0px"> <mtr> <mtd> <msup> <mn>5</mn> <mtable rowspacing="0px" columnspacing="0px"> <mtr> <mtd> <mn>7</mn> </mtd> </mtr> <mtr> <mtd> <mn>6</mn> </mtd> </mtr> </mtable> </msup> </mtd> </mtr> <mtr> <mtd> <msup> <mn>2</mn> <mtable rowspacing="0px" columnspacing="0px"> <mtr> <mtd> <mn>4</mn> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> </mtr> </mtable> </msup> </mtd> </mtr> </mtable> </msup> </msubsup> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>y</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mi>x</mi> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mfrac> <mrow> <mrow> <mi>x</mi> <mo>⁢</mo> <msup> <mi>e</mi> <mi>x</mi> </msup> </mrow> <mo form="infix" lspace="0.000000em" rspace="0.000000em">−</mo> <msup> <mi>e</mi> <mi>x</mi> </msup> <mo form="infix" lspace="0.000000em" rspace="0.000000em">+</mo> <mn>2</mn> </mrow> <msup> <mi>e</mi> <mi>x</mi> </msup> </mfrac> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mi>x</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>1</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mfrac> <mn>2</mn> <msup> <mi>e</mi> <mi>x</mi> </msup> </mfrac> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mtable align="axis" columnalign="right"> <mtr> <mtd> <mrow> <mrow> <mrow> <msub> <mo form="prefix" rspace="0em">ⅅ</mo> <mrow> <mi>x</mi> <mo>​</mo> <mi>x</mi> </mrow> </msub> <mi>y</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mi>y</mi> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <mi>y</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mn>0</mn> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mrow> <msup> <mi>y</mi> <mo form="postfix">′</mo> </msup> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mn>0</mn> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>y</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mi>x</mi> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mrow> <mfrac> <mn>1</mn> <mn>3</mn> </mfrac> <mo>⁢</mo> <msup> <mi>e</mi> <mrow> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mroot> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>1</mn> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mn>3</mn> </mroot> </mrow> <mo>⁢</mo> <mi>x</mi> </mrow> </msup> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> <mo>⁢</mo> <msup> <mi>e</mi> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>⁢</mo> <mroot> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>1</mn> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mn>3</mn> </mroot> <mo>⁢</mo> <mi>x</mi> </mrow> </msup> <mo>⁢</mo> <mrow> <mi mathcolor="gray">cos</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>⁢</mo> <msqrt> <mn>3</mn> </msqrt> <mo>⁢</mo> <mroot> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>1</mn> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mn>3</mn> </mroot> <mo>⁢</mo> <mi>x</mi> </mrow> </mrow> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>y</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mi>t</mi> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mn>2</mn> <mo>⁢</mo> <mrow> <mi mathcolor="gray">tan</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mrow> <mn>2</mn> <mo>⁢</mo> <mi>t</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>4</mn> </mfrac> </mstyle> </mrow> <mo>⁢</mo> <mi>π</mi> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>ℱ</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mtable align="axis"> <mtr> <mtd> <msup> <mi>e</mi> <mrow> <mn>2</mn> <mo>⁢</mo> <mi>π</mi> <mo>⁢</mo> <mi>i</mi> <mo>⁢</mo> <mi>x</mi> </mrow> </msup> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> <mo>⁢</mo> <mi>π</mi> <mo>⁢</mo> <mrow> <mi mathcolor="gray">Dirac</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mi>x</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>2</mn> <mo>⁢</mo> <mi>π</mi> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> </mtd> </mtr> </mtable> <mo form="infix" lspace="0.166667em" rspace="0.000000em">,</mo> <mi>x</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>s</mi> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mtable align="axis"> <mtr> <mtd> <mrow> <mn>2</mn> <mo>⁢</mo> <mi>π</mi> <mo>⁢</mo> <mrow> <mi mathcolor="gray">Dirac</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mi>s</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>2</mn> <mo>⁢</mo> <mi>π</mi> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mn>2</mn> <mo>⁢</mo> <mi>π</mi> <mo>⁢</mo> <msup> <mi>e</mi> <mrow> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>2</mn> </mrow> <mo>⁢</mo> <mi>i</mi> <mo>⁢</mo> <mi>π</mi> <mo>⁢</mo> <mi>s</mi> </mrow> </msup> </mrow> </mtd> </mtr> </mtable> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" mathbackground="transparent"> <mtable> <mtr> <mtd groupalign="right center left"> <maligngroup/> <mrow> <mi>x</mi> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <maligngroup/> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd groupalign="right center left"> <maligngroup/> <mrow> <mrow> <mi>x</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mn>3</mn> </mrow> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <maligngroup/> <mn>123</mn> </mrow> </mtd> </mtr> </mtable> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mtable align="axis" columnalign="right right right right"> <mtr> <mtd> <mi>t</mi> </mtd> <mtd> <mi>x</mi> </mtd> <mtd> <mi>y</mi> </mtd> <mtd> <mi>z</mi> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1.0000</mn> </mtd> <mtd> <mn>1.0000</mn> </mtd> <mtd> <mn>1.0000</mn> </mtd> </mtr> <mtr> <mtd> <mn>.1</mn> </mtd> <mtd> <mn>1.1158</mn> </mtd> <mtd> <mn>1.0938</mn> </mtd> <mtd> <mn>.8842</mn> </mtd> </mtr> <mtr> <mtd> <mn>.2</mn> </mtd> <mtd> <mn>1.2668</mn> </mtd> <mtd> <mn>1.1695</mn> </mtd> <mtd> <mn>.7332</mn> </mtd> </mtr> <mtr> <mtd> <mn>.3</mn> </mtd> <mtd> <mn>1.4582</mn> </mtd> <mtd> <mn>1.2173</mn> </mtd> <mtd> <mn>.5418</mn> </mtd> </mtr> <mtr> <mtd> <mn>.4</mn> </mtd> <mtd> <mn>1.6953</mn> </mtd> <mtd> <mn>1.2253</mn> </mtd> <mtd> <mn>.3047</mn> </mtd> </mtr> <mtr> <mtd> <mn>.5</mn> </mtd> <mtd> <mn>1.9830</mn> </mtd> <mtd> <mn>1.1791</mn> </mtd> <mtd> <mn>.0170</mn> </mtd> </mtr> <mtr> <mtd> <mn>.6</mn> </mtd> <mtd> <mn>2.3256</mn> </mtd> <mtd> <mn>1.0619</mn> </mtd> <mtd> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>.3256</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>.7</mn> </mtd> <mtd> <mn>2.7265</mn> </mtd> <mtd> <mn>.8542</mn> </mtd> <mtd> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>.7265</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>.8</mn> </mtd> <mtd> <mn>3.1873</mn> </mtd> <mtd> <mn>.5344</mn> </mtd> <mtd> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>1.1873</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>.9</mn> </mtd> <mtd> <mn>3.7077</mn> </mtd> <mtd> <mn>.0777</mn> </mtd> <mtd> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>1.7077</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1.0</mn> </mtd> <mtd> <mn>4.2842</mn> </mtd> <mtd> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>.5424</mn> </mrow> </mtd> <mtd> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>2.2842</mn> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <msub> <mi>K</mi> <mi>v</mi> </msub> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi>z</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <msub> <mi mathcolor="gray">BesselK</mi> <mi>v</mi> </msub> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mi>z</mi> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mrow> <msup> <mi>z</mi> <mn>2</mn> </msup> <mo>⁢</mo> <mfrac> <mrow> <msup> <mo form="prefix" rspace="0em">ⅆ</mo> <mn>2</mn> </msup> <mi>w</mi> </mrow> <mrow> <mo form="prefix" rspace="0em">ⅆ</mo> <msup> <mi>z</mi> <mn>2</mn> </msup> </mrow> </mfrac> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mi>z</mi> <mo>⁢</mo> <mfrac> <mrow> <mo form="prefix" rspace="0em">ⅆ</mo> <mi>w</mi> </mrow> <mrow> <mo form="prefix" rspace="0em">ⅆ</mo> <mi>z</mi> </mrow> </mfrac> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <msup> <mi>z</mi> <mn>2</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <msup> <mi>v</mi> <mn>2</mn> </msup> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mo>⁢</mo> <mi>w</mi> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>0</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mfrac> <mrow> <msup> <mo form="prefix" rspace="0em">∂</mo> <mn>2</mn> </msup> <mrow> <mi>u</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>x</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>y</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> </mrow> <mrow> <mo form="prefix" rspace="0em">∂</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mfrac> <mrow> <msup> <mo form="prefix" rspace="0em">∂</mo> <mn>2</mn> </msup> <mrow> <mi>u</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>x</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>y</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> </mrow> <mrow> <mo form="prefix" rspace="0em">∂</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> </mrow> </mfrac> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>0</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>y</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mi>t</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>x</mi> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mrow> <msub> <mi>F</mi> <mn>1</mn> </msub> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mi>x</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mi>a</mi> <mo>⁢</mo> <mi>t</mi> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <msub> <mi>F</mi> <mn>2</mn> </msub> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mi>x</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mi>a</mi> <mo>⁢</mo> <mi>t</mi> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mtable align="axis" columnlines="solid none" columnalign="left center right"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>2</mn> </mtd> <mtd> <mn>3</mn> </mtd> </mtr> <mtr> <mtd> <mn>4</mn> </mtd> <mtd> <mn>5</mn> </mtd> <mtd> <mn>6</mn> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mrow> <mn>2</mn> <mo>⁢</mo> <mi>x</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mn>1</mn> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>5</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" mathbackground="transparent"> <mtable> <mtr> <mtd groupalign="right center left"> <maligngroup/> <mrow> <mn>1</mn> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <maligngroup/> <mn>3</mn> </mrow> </mtd> </mtr> <mtr> <mtd groupalign="right center left"> <maligngroup/> <mrow> <mn>9</mn> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <maligngroup/> <mn>7</mn> </mrow> </mtd> </mtr> </mtable> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" mathbackground="transparent"> <mtable> <mtr> <mtd groupalign="right left"> <maligngroup/> <mrow> <mi>a</mi> <maligngroup/> <mo>⁢</mo> <mi>b</mi> </mrow> </mtd> </mtr> <mtr> <mtd groupalign="right left"> <maligngroup/> <mrow> <mi>c</mi> <maligngroup/> <mo>⁢</mo> <mi>d</mi> </mrow> </mtd> </mtr> <mtr> <mtd groupalign="right left"> <maligngroup/> <mrow> <mi>e</mi> <maligngroup/> <mo>⁢</mo> <mi>f</mi> </mrow> </mtd> </mtr> </mtable> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" mathbackground="transparent"> <mtable> <mtr> <mtd groupalign="center"> <maligngroup/> <mrow> <mrow> <mi>x</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>2</mn> <mo>⁢</mo> <mi>y</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>3</mn> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>5</mn> </mrow> </mtd> </mtr> <mtr> <mtd groupalign="center"> <maligngroup/> <mrow> <mrow> <mrow> <mn>4</mn> <mo>⁢</mo> <mi>x</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mi>y</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>5</mn> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>98</mn> </mrow> </mtd> </mtr> </mtable> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" mathbackground="transparent"> <mtable> <mtr> <mtd groupalign="right center left"> <maligngroup/> <mrow> <mi>x</mi> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <maligngroup/> <mi>z</mi> </mrow> </mtd> </mtr> <mtr> <mtd groupalign="right center left"> <maligngroup/> <mrow> <mn>1</mn> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <maligngroup/> <mn>3</mn> </mrow> </mtd> </mtr> </mtable> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" mathbackground="transparent"> <mtable> <mtr> <mtd groupalign="right left"> <maligngroup/> <mrow> <msub> <mi>A</mi> <mn>1</mn> </msub> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mrow> <msub> <mi>N</mi> <mn>0</mn> </msub> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>λ</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">;</mo> <msup> <mi>Ω</mi> <mo form="postfix">′</mo> </msup> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mi>φ</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>λ</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">;</mo> <msup> <mi>Ω</mi> <mo form="postfix">′</mo> </msup> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> </mrow> </mrow> <mtext>,</mtext> </mtd> </mtr> <mtr> <mtd groupalign="right left"> <maligngroup/> <mrow> <msub> <mi>A</mi> <mn>2</mn> </msub> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mrow> <mi>φ</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>λ</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">;</mo> <msup> <mi>Ω</mi> <mo form="postfix">′</mo> </msup> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mi>φ</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>λ</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">;</mo> <mi>Ω</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> </mrow> </mrow> <mtext>,</mtext> </mtd> </mtr> <mtr> <mtd groupalign="right left"> <maligngroup/> <mrow> <msub> <mi>A</mi> <mn>3</mn> </msub> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mi mathvariant="script">N</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>λ</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">;</mo> <mi>ω</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> </mrow> <mtext>.</mtext> </mtd> </mtr> </mtable> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" mathbackground="transparent"> <mtable> <mtr> <mtd groupalign="center"> <maligngroup/> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> </mtd> </mtr> <mtr> <mtd groupalign="center"> <maligngroup/> <mrow> <mi mathcolor="gray">cos</mi> <mo rspace="0.166667em">⁡</mo> <mi>γ</mi> </mrow> </mtd> </mtr> </mtable> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" lspace="0.5em" rspace="0.5em">{</mo> <mtable columnalign="left"> <mtr> <mtd> <mi>x</mi> </mtd> <mtd> <mtext mathcolor="black">if </mtext> <mrow> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em"><</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mi>x</mi> </mrow> </mtd> <mtd> <mtext mathcolor="black">if </mtext> <mrow> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">≥</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mtable> <mtr> <mtd groupalign="right left"> <maligngroup/> <mrow> <mi>L</mi> <mo>⁢</mo> <mi>M</mi> <maligngroup/> <mo>⁢</mo> <mi>R</mi> <mo>⁢</mo> <mi>M</mi> </mrow> </mtd> </mtr> <mtr> <mtd groupalign="right left"> <maligngroup/> <mrow> <mi>L</mi> <mo>⁢</mo> <mi>M</mi> <maligngroup/> <mo>⁢</mo> <mi>R</mi> <mo>⁢</mo> <mi>M</mi> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mtable> <mtr> <mtd groupalign="center"> <maligngroup/> <mrow> <mi>M</mi> <mo>⁢</mo> <mi>A</mi> <mo>⁢</mo> <mi>T</mi> <mo>⁢</mo> <mi>H</mi> </mrow> </mtd> </mtr> <mtr> <mtd groupalign="center"> <maligngroup/> <mrow> <mi>M</mi> <mo>⁢</mo> <mi>A</mi> <mo>⁢</mo> <mi>T</mi> <mo>⁢</mo> <mi>H</mi> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mtext>⋮</mtext> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo form="prefix" rspace="0em">∇×</mo> <mi>F</mi> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>0</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" rspace="0em">∇·</mo> <mi>F</mi> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo form="prefix" rspace="0em">∇·∇</mo> <mi>F</mi> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mrow> <msup> <mo form="prefix" lspace="0.277778em" rspace="0em">∇</mo> <mn>2</mn> </msup> <mi>F</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mn>7</mn> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mi>A</mi> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo form="prefix" rspace="0em">∇×</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mrow> <mi>x</mi> <mo>⁢</mo> <mi>y</mi> </mrow> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mrow> <mi>y</mi> <mo>⁢</mo> <mi>z</mi> </mrow> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mrow> <mi>z</mi> <mo>⁢</mo> <mi>x</mi> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.388889em">=</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">[</mo> <mtable align="axis"> <mtr> <mtd> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mi>y</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mi>z</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mi>x</mi> </mrow> </mtd> </mtr> </mtable> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">]</mo> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo form="prefix" rspace="0em">∇×</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>y</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>z</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>x</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>1</mn> </mrow> <mo form="infix" lspace="0.000000em" rspace="0.222222em">,</mo> <mrow> <mo form="prefix" lspace="0.222222em" rspace="0em">−</mo> <mn>1</mn> </mrow> <mo form="infix" lspace="0.000000em" rspace="0.222222em">,</mo> <mrow> <mo form="prefix" lspace="0.222222em" rspace="0em">−</mo> <mn>1</mn> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">≠</mo> <mn>0</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mstyle fontweight="bold"> <mrow> <mrow> <mi>x</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>y</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>α</mi> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>102</mn> </mrow> </mstyle> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi mathvariant="bold">a</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi mathvariant="bold">b</mi> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mi mathvariant="bold">c</mi> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>x</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mn>1</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>x</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi mathvariant="bold">x</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mrow> <mstyle fontweight="bold"> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> </mstyle> </mrow> <mn>1</mn> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>123</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi mathvariant="italic">T</mi> <mo>⁢</mo> <mi mathvariant="italic">h</mi> <mo>⁢</mo> <mi mathvariant="italic">e</mi> <mo>⁢</mo> <mi mathvariant="italic">q</mi> <mo>⁢</mo> <mi mathvariant="italic">u</mi> <mo>⁢</mo> <mi mathvariant="italic">i</mi> <mo>⁢</mo> <mi mathvariant="italic">c</mi> <mo>⁢</mo> <mi mathvariant="italic">k</mi> <mo>⁢</mo> <mrow> <mstyle fontstyle="italic"> <mi>b</mi> </mstyle> </mrow> <mo>⁢</mo> <mrow> <mstyle fontstyle="italic"> <mi>r</mi> </mstyle> </mrow> <mo>⁢</mo> <mrow> <mstyle fontstyle="italic"> <mi>o</mi> </mstyle> </mrow> <mo>⁢</mo> <mrow> <mstyle fontstyle="italic"> <mi>w</mi> </mstyle> </mrow> <mo>⁢</mo> <mrow> <mstyle fontstyle="italic"> <mi>n</mi> </mstyle> </mrow> <mo>⁢</mo> <mi>f</mi> <mo>⁢</mo> <mi>o</mi> <mo>⁢</mo> <mi>x</mi> <mo>⁢</mo> <mi>j</mi> <mo>⁢</mo> <mi>u</mi> <mo>⁢</mo> <mi>m</mi> <mo>⁢</mo> <mi>p</mi> <mo>⁢</mo> <mi>s</mi> <mo>⁢</mo> <mi mathvariant="bold">o</mi> <mo>⁢</mo> <mi mathvariant="bold">v</mi> <mo>⁢</mo> <mi mathvariant="bold">e</mi> <mo>⁢</mo> <mi mathvariant="bold">r</mi> <mo>⁢</mo> <mrow> <mstyle fontweight="normal"> <mi>t</mi> </mstyle> </mrow> <mo>⁢</mo> <mrow> <mstyle fontweight="normal"> <mi>h</mi> </mstyle> </mrow> <mo>⁢</mo> <mrow> <mstyle fontweight="normal"> <mi>e</mi> </mstyle> </mrow> <mo>⁢</mo> <mi mathvariant="sans-serif">l</mi> <mo>⁢</mo> <mi mathvariant="sans-serif">a</mi> <mo>⁢</mo> <mi mathvariant="sans-serif">z</mi> <mo>⁢</mo> <mi mathvariant="sans-serif">y</mi> <mo>⁢</mo> <mi mathvariant="monospace">d</mi> <mo>⁢</mo> <mi mathvariant="monospace">o</mi> <mo>⁢</mo> <mi mathvariant="monospace">g</mi> </mrow> <mrow> <mstyle fontstyle="italic"> <mtext>.</mtext> </mstyle> </mrow> <mrow> <mrow> <mstyle fontweight="bold"> <mi>T</mi> </mstyle> </mrow> <mo>⁢</mo> <mrow> <mstyle fontweight="bold"> <mi>h</mi> </mstyle> </mrow> <mo>⁢</mo> <mrow> <mstyle fontweight="bold"> <mi>e</mi> </mstyle> </mrow> <mo>⁢</mo> <mrow> <mstyle fontweight="bold"> <mi>e</mi> </mstyle> </mrow> <mo>⁢</mo> <mrow> <mstyle fontweight="bold"> <mi>n</mi> </mstyle> </mrow> <mo>⁢</mo> <mrow> <mstyle fontweight="bold"> <mi>d</mi> </mstyle> </mrow> </mrow> <mrow> <mstyle fontweight="bold"> <mtext>.</mtext> </mstyle> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mrow> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <mo form="prefix" rspace="0em">∂</mo> <mi>f</mi> </mrow> <mrow> <mo form="prefix" rspace="0em">∂</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> </mrow> </mfrac> </mstyle> </mrow> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <msub> <mi>c</mi> <mn>1</mn> </msub> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <msub> <mi>c</mi> <mn>2</mn> </msub> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>…</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <msub> <mi>c</mi> <mi>n</mi> </msub> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.166667em" rspace="0.166667em">,</mo> <mrow> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <mo form="prefix" rspace="0em">∂</mo> <mi>f</mi> </mrow> <mrow> <mo form="prefix" rspace="0em">∂</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> </mfrac> </mstyle> </mrow> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <msub> <mi>c</mi> <mn>1</mn> </msub> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <msub> <mi>c</mi> <mn>2</mn> </msub> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>…</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <msub> <mi>c</mi> <mi>n</mi> </msub> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.166667em" rspace="0.000000em">,</mo> <mi>…</mi> <mo form="infix" lspace="0.000000em" rspace="0.166667em">,</mo> <mrow> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <mo form="prefix" rspace="0em">∂</mo> <mi>f</mi> </mrow> <mrow> <mo form="prefix" rspace="0em">∂</mo> <msub> <mi>x</mi> <mrow> <mi>n</mi> <mo>​</mo> <mn>1</mn> </mrow> </msub> </mrow> </mfrac> </mstyle> </mrow> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <msub> <mi>c</mi> <mn>1</mn> </msub> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <msub> <mi>c</mi> <mn>2</mn> </msub> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>…</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <msub> <mi>c</mi> <mi>n</mi> </msub> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo form="prefix" rspace="0em">∇</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mrow> <mi>c</mi> <mo>⁢</mo> <mi>u</mi> <mo>⁢</mo> <mi>v</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <msup> <mi>v</mi> <mn>2</mn> </msup> <mo>⁢</mo> <mi>w</mi> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mrow> <mi>u</mi> <mo>⁢</mo> <mi>v</mi> </mrow> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mrow> <mi>c</mi> <mo>⁢</mo> <mi>v</mi> </mrow> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mrow> <mrow> <mi>c</mi> <mo>⁢</mo> <mi>u</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>2</mn> <mo>⁢</mo> <mi>v</mi> <mo>⁢</mo> <mi>w</mi> </mrow> </mrow> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <msup> <mi>v</mi> <mn>2</mn> </msup> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" mathbackground="transparent"> <mtable> <mtr> <mtd groupalign="right center left"> <maligngroup/> <mrow> <mrow> <msub> <mi>D</mi> <mrow> <mstyle fontweight="bold"> <mi>u</mi> </mstyle> </mrow> </msub> <mo>⁢</mo> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mi>a</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>b</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>c</mi> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <maligngroup/> <mrow> <mrow> <mo form="prefix" lspace="0.277778em" rspace="0em">∇</mo> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mi>a</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>b</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>c</mi> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">⋅</mo> <mi mathvariant="bold">u</mi> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd groupalign="right center left"> <maligngroup/> <maligngroup/> <mo form="infix" lspace="thickmathspace" rspace="0.277778em">=</mo> <maligngroup/> <mrow> <mrow> <mrow> <mfrac> <mrow> <mo form="prefix" rspace="0em">∂</mo> <mi>f</mi> </mrow> <mrow> <mo form="prefix" rspace="0em">∂</mo> <mi>x</mi> </mrow> </mfrac> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mi>a</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>b</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>c</mi> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo>⁢</mo> <msub> <mi>u</mi> <mn>1</mn> </msub> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mrow> <mfrac> <mrow> <mo form="prefix" rspace="0em">∂</mo> <mi>f</mi> </mrow> <mrow> <mo form="prefix" rspace="0em">∂</mo> <mi>y</mi> </mrow> </mfrac> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mi>a</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>b</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>c</mi> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo>⁢</mo> <msub> <mi>u</mi> <mn>2</mn> </msub> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mrow> <mfrac> <mrow> <mo form="prefix" rspace="0em">∂</mo> <mi>f</mi> </mrow> <mrow> <mo form="prefix" rspace="0em">∂</mo> <mi>z</mi> </mrow> </mfrac> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mi>a</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>b</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>c</mi> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo>⁢</mo> <msub> <mi>u</mi> <mn>3</mn> </msub> </mrow> </mrow> </mtd> </mtr> </mtable> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>θ</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">∈</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">{</mo> <mrow> <mrow> <mi>π</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>2</mn> <mo>⁢</mo> <msub> <mi>X</mi> <mn>3</mn> </msub> <mo>⁢</mo> <mi>π</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mi mathcolor="gray">arccos</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mfrac> <mn>1</mn> <mn>7</mn> </mfrac> <mo>⁢</mo> <msqrt> <mn>14</mn> </msqrt> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo form="infix" stretchy="true" minsize="0" lspace="0.555556em" rspace="0.555556em">|</mo> <mrow> <msub> <mi>X</mi> <mn>3</mn> </msub> <mo form="infix" lspace="0.277778em" rspace="0.277778em">∈</mo> <mi>ℤ</mi> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">}</mo> </mrow> </mrow> <mo form="infix" lspace="0.166667em" rspace="0.000000em">,</mo> <mrow> <mi>θ</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">∈</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">{</mo> <mrow> <mrow> <mrow> <mn>2</mn> <mo>⁢</mo> <msub> <mi>X</mi> <mn>4</mn> </msub> <mo>⁢</mo> <mi>π</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mi>π</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mi mathcolor="gray">arccos</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mfrac> <mn>1</mn> <mn>7</mn> </mfrac> <mo>⁢</mo> <msqrt> <mn>14</mn> </msqrt> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo form="infix" stretchy="true" minsize="0" lspace="0.555556em" rspace="0.555556em">|</mo> <mrow> <msub> <mi>X</mi> <mn>4</mn> </msub> <mo form="infix" lspace="0.277778em" rspace="0.277778em">∈</mo> <mi>ℤ</mi> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">}</mo> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>P</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mi>A</mi> <mo>⁢</mo> <msup> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <msup> <mi>A</mi> <mi>T</mi> </msup> <mo>⁢</mo> <mi>A</mi> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>1</mn> </mrow> </msup> <mo>⁢</mo> <msup> <mi>A</mi> <mi>T</mi> </msup> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo mathcolor="gray" form="prefix" rspace="0em">det</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mtable align="axis"> <mtr> <mtd> <mi>x</mi> </mtd> <mtd> <mi>y</mi> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>a</mi> </mtd> <mtd> <mi>b</mi> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mi>a</mi> </mtd> <mtd> <mi>d</mi> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mrow> <mi>x</mi> <mo>⁢</mo> <mi>b</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mi>x</mi> <mo>⁢</mo> <mi>d</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mi>a</mi> <mo>⁢</mo> <mi>d</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mi>a</mi> <mo>⁢</mo> <mi>b</mi> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>0</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mrow> <mi>A</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mi>θ</mi> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo>⁢</mo> <mrow> <mi>A</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mi>θ</mi> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.388889em">=</mo> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">[</mo> <mtable align="axis" columnalign="right right"> <mtr> <mtd> <mrow> <mi mathcolor="gray">cos</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> </mtd> <mtd> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> </mtd> <mtd> <mrow> <mi mathcolor="gray">cos</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> </mtd> </mtr> </mtable> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">]</mo> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">[</mo> <mtable align="axis" columnalign="right right"> <mtr> <mtd> <mrow> <mi mathcolor="gray">cos</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> </mtd> <mtd> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> </mrow> </mtd> <mtd> <mrow> <mi mathcolor="gray">cos</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> </mtd> </mtr> </mtable> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">]</mo> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>J</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi>A</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">[</mo> <mtable align="axis"> <mtr> <mtd> <mrow> <msub> <mi>J</mi> <msub> <mi>n</mi> <mn>1</mn> </msub> </msub> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <msub> <mi>λ</mi> <mn>1</mn> </msub> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mi>⋯</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <msub> <mi>J</mi> <msub> <mi>n</mi> <mn>2</mn> </msub> </msub> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <msub> <mi>λ</mi> <mn>2</mn> </msub> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mtd> <mtd> <mi>⋯</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mtext>⋮</mtext> </mtd> <mtd> <mtext>⋮</mtext> </mtd> <mtd> <mtext>⋱</mtext> </mtd> <mtd> <mtext>⋮</mtext> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mi>⋯</mi> </mtd> <mtd> <mrow> <msub> <mi>J</mi> <msub> <mi>n</mi> <mi>k</mi> </msub> </msub> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <msub> <mi>λ</mi> <mi>k</mi> </msub> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">]</mo> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo mathcolor="gray" form="prefix" rspace="0.388889em">det</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mtable align="axis"> <mtr> <mtd> <mrow> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>4</mn> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>X</mi> </mrow> </mtd> <mtd> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>4</mn> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>X</mi> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>4</mn> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>X</mi> </mrow> </mtd> </mtr> </mtable> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <msup> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mi>X</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>4</mn> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mn>3</mn> </msup> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">{</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mtable align="axis"> <mtr> <mtd> <mrow> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mfrac> <mn>1</mn> <mn>6</mn> </mfrac> <mo>⁢</mo> <msqrt> <mn>33</mn> </msqrt> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">}</mo> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">↔</mo> <mrow> <mfrac> <mn>5</mn> <mn>2</mn> </mfrac> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mo>⁢</mo> <msqrt> <mn>33</mn> </msqrt> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">∥</mo> <mi>A</mi> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">∥</mo> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <munder> <mo mathcolor="gray" form="prefix" movablelimits="false" lspace="0.277778em" rspace="0.166667em">max</mo> <mrow> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">≠</mo> <mn>0</mn> </mrow> </munder> <mfrac> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">∥</mo> <mrow> <mi>A</mi> <mo>⁢</mo> <mi>x</mi> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">∥</mo> </mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">∥</mo> <mi>x</mi> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">∥</mo> </mrow> </mfrac> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mtable align="axis"> <mtr> <mtd> <msub> <mi>a</mi> <mrow> <mn>1</mn> <mo>​</mo> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mrow> <mn>1</mn> <mo>​</mo> <mn>2</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mrow> <mn>2</mn> <mo>​</mo> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mrow> <mn>2</mn> <mo>​</mo> <mn>2</mn> </mrow> </msub> </mtd> </mtr> </mtable> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.388889em">+</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mtable align="axis"> <mtr> <mtd> <msub> <mi>b</mi> <mrow> <mn>1</mn> <mo>​</mo> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>b</mi> <mrow> <mn>1</mn> <mo>​</mo> <mn>2</mn> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>b</mi> <mrow> <mn>2</mn> <mo>​</mo> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>b</mi> <mrow> <mn>2</mn> <mo>​</mo> <mn>2</mn> </mrow> </msub> </mtd> </mtr> </mtable> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.388889em">=</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mtable align="axis"> <mtr> <mtd> <mrow> <msub> <mi>a</mi> <mrow> <mn>1</mn> <mo>​</mo> <mn>1</mn> </mrow> </msub> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <msub> <mi>b</mi> <mrow> <mn>1</mn> <mo>​</mo> <mn>1</mn> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>a</mi> <mrow> <mn>1</mn> <mo>​</mo> <mn>2</mn> </mrow> </msub> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <msub> <mi>b</mi> <mrow> <mn>1</mn> <mo>​</mo> <mn>2</mn> </mrow> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>a</mi> <mrow> <mn>2</mn> <mo>​</mo> <mn>1</mn> </mrow> </msub> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <msub> <mi>b</mi> <mrow> <mn>2</mn> <mo>​</mo> <mn>1</mn> </mrow> </msub> </mrow> </mtd> <mtd> <mrow> <msub> <mi>a</mi> <mrow> <mn>2</mn> <mo>​</mo> <mn>2</mn> </mrow> </msub> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <msub> <mi>b</mi> <mrow> <mn>2</mn> <mo>​</mo> <mn>2</mn> </mrow> </msub> </mrow> </mtd> </mtr> </mtable> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">[</mo> <mtable align="axis"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mn>4</mn> </mtd> <mtd> <mn>3</mn> </mtd> </mtr> </mtable> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">]</mo> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <msup> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">[</mo> <mtable align="axis"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mn>4</mn> </mtd> <mtd> <mn>3</mn> </mtd> </mtr> </mtable> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">]</mo> </mrow> <mn>2</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>5</mn> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">[</mo> <mtable align="axis"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mn>4</mn> </mtd> <mtd> <mn>3</mn> </mtd> </mtr> </mtable> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">]</mo> </mrow> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>2</mn> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">[</mo> <mtable align="axis"> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>2</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>4</mn> </mrow> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">]</mo> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <munder> <mo mathcolor="gray" form="prefix" movablelimits="true" lspace="0.277778em" rspace="0.166667em">lim</mo> <mrow> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>1</mn> </mrow> </munder> <mrow> <munderover> <mo form="prefix" movablelimits="true" largeop="false" stretchy="false" lspace="0.166667em" rspace="0em">∑</mo> <mn>1</mn> <mn>2</mn> </munderover> <mi>a</mi> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <msubsup> <mo form="prefix" largeop="false" stretchy="true" maxsize="1.4" minsize="1.4" rspace="0em">∫</mo> <mi>a</mi> <mi>b</mi> </msubsup> <mrow> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi>x</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.166667em" rspace="0em">ⅆ</mo> <mi>x</mi> </mrow> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <munder> <mo mathcolor="gray" form="prefix" movablelimits="false" lspace="0.277778em" rspace="0.166667em">lim</mo> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">∥</mo> <mi>P</mi> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">∥</mo> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">→</mo> <mn>0</mn> </mrow> </munder> <mrow> <munderover> <mo form="prefix" movablelimits="false" largeop="false" stretchy="true" maxsize="1.4" minsize="1.4" lspace="0.166667em" rspace="0em">∑</mo> <mrow> <mi>i</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <msub> <mover> <mi>x</mi> <mo stretchy="true" accent="true">¯</mo> </mover> <mi>i</mi> </msub> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.166667em" rspace="0em">Δ</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> </mrow> </mrow> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <msubsup> <mo form="prefix" largeop="false" stretchy="false" rspace="0em">∫</mo> <mi>a</mi> <mi>b</mi> </msubsup> <mrow> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi>x</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.166667em" rspace="0em">ⅆ</mo> <mi>x</mi> </mrow> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <munder> <mo mathcolor="gray" form="prefix" movablelimits="true" lspace="0.277778em" rspace="0.166667em">lim</mo> <mrow> <mi>n</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">→</mo> <mi>∞</mi> </mrow> </munder> <mrow> <mfrac> <mrow> <mi>b</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">−</mo> <mi>a</mi> </mrow> <mi>n</mi> </mfrac> <mo>⁢</mo> <mrow> <munderover> <mo form="prefix" movablelimits="true" largeop="false" stretchy="false" lspace="0.166667em" rspace="0em">∑</mo> <mrow> <mi>i</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mi>a</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mi>i</mi> <mo>⁢</mo> <mfrac> <mrow> <mi>b</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">−</mo> <mi>a</mi> </mrow> <mi>n</mi> </mfrac> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <msubsup> <mo form="prefix" largeop="false" stretchy="false" rspace="0em">∫</mo> <mn>0</mn> <mn>2</mn> </msubsup> <mrow> <msup> <mi>x</mi> <mn>5</mn> </msup> <mo>⁢</mo> <msqrt> <mrow> <msup> <mi>x</mi> <mn>3</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mn>1</mn> </mrow> </msqrt> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.000000em" rspace="0em">ⅆ</mo> <mi>x</mi> </mrow> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <msubsup> <mo form="prefix" largeop="false" stretchy="false" lspace="0.277778em" rspace="0em">∫</mo> <mn>1</mn> <mn>3</mn> </msubsup> <mrow> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> <mo>⁢</mo> <mi>u</mi> <mo>⁢</mo> <mfrac> <msqrt> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <msup> <mi>u</mi> <mn>2</mn> </msup> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </msqrt> <msup> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <msup> <mi>u</mi> <mn>2</mn> </msup> <mo form="infix" lspace="0.000000em" rspace="0.000000em">−</mo> <mn>1</mn> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> </msup> </mfrac> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mrow> <msup> <mi>u</mi> <mn>2</mn> </msup> <mo>⁢</mo> <msup> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <msup> <mi>u</mi> <mn>2</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>1</mn> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> </msup> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <msup> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <msup> <mi>u</mi> <mn>2</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>1</mn> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mfrac> <mn>2</mn> <mn>3</mn> </mfrac> </msup> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.166667em" rspace="0em">ⅆ</mo> <mi>u</mi> </mrow> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo form="prefix" largeop="false" stretchy="true" maxsize="1.4" minsize="1.4" rspace="0em">∫</mo> <mrow> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>g</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi>x</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo lspace="0.333333em">⁢</mo> <mrow> <msup> <mi>g</mi> <mo form="postfix">′</mo> </msup> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi>x</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.166667em" rspace="0em">ⅆ</mo> <mi>x</mi> </mrow> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mo form="prefix" largeop="false" stretchy="true" maxsize="1.4" minsize="1.4" lspace="0.277778em" rspace="0em">∫</mo> <mrow> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi>u</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.166667em" rspace="0em">ⅆ</mo> <mi>u</mi> </mrow> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mn>2</mn> <mo>⁢</mo> <mrow> <munderover> <mo form="prefix" movablelimits="true" largeop="false" stretchy="false" lspace="0.166667em" rspace="0em">∑</mo> <mrow> <mi>n</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>1</mn> </mrow> <mn>100</mn> </munderover> <mrow> <mi>n</mi> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>n</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>1</mn> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <munder> <mo mathcolor="gray" form="prefix" movablelimits="false" rspace="0.166667em">lim</mo> <mrow> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">→</mo> <mn>0</mn> </mrow> </munder> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mfrac> <mn>1</mn> <mi>x</mi> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="thickmathspace">=</mo> <mrow> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>1</mn> </mrow> <mo form="infix" lspace="0.000000em" rspace="0.000000em">..</mo> <mn>1</mn> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>h</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>i</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>j</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mn>2</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mi>j</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> <mo>⁢</mo> <mrow> <mi>g</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi>i</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>j</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>1</mn> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> <mo>⁢</mo> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>g</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi>i</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>△</mi> <mo form="infix" lspace="0.000000em" rspace="0.166667em">:</mo> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">[</mo> <mrow> <mn>0</mn> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mn>1</mn> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">]</mo> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">→</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">[</mo> <mrow> <mn>0</mn> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mn>1</mn> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">]</mo> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mn>0</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">▽</mo> <mi>x</mi> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mi>x</mi> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>x</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">△</mo> <mi>y</mi> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <msup> <mi>h</mi> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>1</mn> </mrow> </msup> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mrow> <mi>h</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mi>x</mi> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo>⁢</mo> <mrow> <mi>h</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mi>y</mi> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>x</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">△</mo> <mi>y</mi> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <msup> <mi>f</mi> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>1</mn> </mrow> </msup> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mo mathcolor="gray" form="prefix" rspace="0em">max</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">{</mo> <mrow> <mrow> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mi>x</mi> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mi>y</mi> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>1</mn> </mrow> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mn>0</mn> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">}</mo> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>x</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">▽</mo> <mi>y</mi> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mi>η</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mrow> <mi>η</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mi>x</mi> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">△</mo> <mrow> <mi>η</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mi>y</mi> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>x</mi> <mo>⁢</mo> <mrow> <msub> <mo form="infix" lspace="0.222222em" rspace="0.222222em">△</mo> <mn>0</mn> </msub> <mi>y</mi> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">{</mo> <mtable align="axis"> <mtr> <mtd> <mrow> <mi>x</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">∧</mo> <mi>y</mi> </mrow> </mtd> <mtd> <mtext mathcolor="black">if</mtext> </mtd> <mtd> <mrow> <mi>x</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">∨</mo> <mrow> <mi>y</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>1</mn> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mtext mathcolor="black">if</mtext> </mtd> <mtd> <mrow> <mi>x</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">∨</mo> <mrow> <mi>y</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em"><</mo> <mn>1</mn> </mrow> </mrow> </mtd> </mtr> </mtable> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace"/> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <munder> <mo mathcolor="gray" form="prefix" movablelimits="true" rspace="0.166667em">lim</mo> <mrow> <mi>a</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">→</mo> <msup> <mn>1</mn> <mo>+</mo> </msup> </mrow> </munder> <mrow> <msub> <mi mathcolor="gray">log</mi> <mi>a</mi> </msub> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">[</mo> <mrow> <mn>1</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <msup> <mi>a</mi> <mi>x</mi> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>1</mn> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <msup> <mi>a</mi> <mi>y</mi> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>1</mn> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mrow> <mi>a</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>1</mn> </mrow> </mfrac> </mstyle> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">]</mo> </mrow> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <munder> <mo mathcolor="gray" form="prefix" movablelimits="true" lspace="0.277778em" rspace="0.166667em">lim</mo> <mrow> <mi>a</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">→</mo> <msup> <mn>1</mn> <mo>−</mo> </msup> </mrow> </munder> <mrow> <msub> <mi mathcolor="gray">log</mi> <mi>a</mi> </msub> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">[</mo> <mrow> <mn>1</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <msup> <mi>a</mi> <mi>x</mi> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>1</mn> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <msup> <mi>a</mi> <mi>y</mi> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>1</mn> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mrow> <mi>a</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>1</mn> </mrow> </mfrac> </mstyle> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">]</mo> </mrow> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mi>x</mi> <mo>⁢</mo> <mi>y</mi> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>g</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi>x</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mi mathcolor="gray">exp</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <mn>1</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <msup> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mn>1</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mi>x</mi> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mi>a</mi> </msup> </mrow> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <msup> <mn>2</mn> <mi>a</mi> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>1</mn> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mo>⁢</mo> <msup> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mn>1</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mi>x</mi> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mi>a</mi> </msup> </mrow> </mfrac> </mstyle> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo mathcolor="gray" form="prefix" rspace="0em">Aut</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi mathvariant="bold">I</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">{</mo> <mrow> <mi>f</mi> <mo form="infix" lspace="0.000000em" rspace="0.166667em">:</mo> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">[</mo> <mrow> <mn>0</mn> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mn>1</mn> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">]</mo> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">→</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">[</mo> <mrow> <mn>0</mn> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mn>1</mn> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">]</mo> </mrow> </mrow> </mrow> <mspace width="thickmathspace"/> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">|</mo> <mtable align="axis" columnalign="left"> <mtr> <mtd> <mi>f</mi> <mtext mathcolor="black"> is one-to-one and onto, and</mtext> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">≤</mo> <mi>y</mi> </mrow> <mtext mathcolor="black"> implies </mtext> <mrow> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mi>x</mi> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">≤</mo> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mi>y</mi> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> </mtd> </mtr> </mtable> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace"/> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">}</mo> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <msup> <mi>r</mi> <mn>2</mn> </msup> </mrow> <mo form="infix" lspace="0.000000em" rspace="0.166667em">,</mo> <mtext>  </mtext> <mrow> <mrow> <mi mathcolor="gray">tan</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mi>y</mi> <mi>x</mi> </mfrac> </mstyle> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <msqrt> <mn>2</mn> </msqrt> <mo>⁢</mo> <msqrt> <mrow> <mn>1</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <msup> <mi>t</mi> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">[</mo> <mrow> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mn>2</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>t</mi> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> <mo>⁢</mo> <mn>10</mn> <mo>⁢</mo> <mrow> <mi mathcolor="gray">cos</mi> <mo rspace="0.166667em">⁡</mo> <mi>t</mi> </mrow> </mrow> <mo form="infix" lspace="0.000000em" rspace="0.555556em">,</mo> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mn>2</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mi mathcolor="gray">cos</mi> <mo rspace="0.166667em">⁡</mo> <mi>t</mi> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> <mo>⁢</mo> <mn>10</mn> <mo>⁢</mo> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>t</mi> </mrow> </mrow> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mrow> <mn>3</mn> <mo>⁢</mo> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mn>3</mn> <mo>⁢</mo> <mi>t</mi> </mrow> </mrow> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">]</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">{</mo> <mrow> <mrow> <mi>t</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>0</mn> </mrow> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mrow> <mi>s</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>0</mn> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">}</mo> </mrow> <mo form="infix" lspace="0.166667em" rspace="0.166667em">,</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">{</mo> <mrow> <mrow> <mi>t</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mi>π</mi> </mrow> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mrow> <mi>s</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mi>π</mi> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">}</mo> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mtable frame="solid" framespacing="0.8em 1.0ex"> <mtr> <mtd> <mrow> <mtable align="axis"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>2</mn> </mtd> <mtd> <mn>3</mn> </mtd> <mtd> <mn>4</mn> </mtd> <mtd> <mn>5</mn> </mtd> <mtd> <mn>6</mn> </mtd> <mtd> <mn>7</mn> </mtd> <mtd> <mn>8</mn> </mtd> <mtd> <mn>9</mn> </mtd> <mtd> <mn>10</mn> </mtd> </mtr> <mtr> <mtd> <mn>2</mn> </mtd> <mtd> <mn>4</mn> </mtd> <mtd> <mn>6</mn> </mtd> <mtd> <mn>8</mn> </mtd> <mtd> <mn>10</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>3</mn> </mtd> <mtd> <mn>5</mn> </mtd> <mtd> <mn>7</mn> </mtd> <mtd> <mn>9</mn> </mtd> </mtr> <mtr> <mtd> <mn>3</mn> </mtd> <mtd> <mn>6</mn> </mtd> <mtd> <mn>9</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>4</mn> </mtd> <mtd> <mn>7</mn> </mtd> <mtd> <mn>10</mn> </mtd> <mtd> <mn>2</mn> </mtd> <mtd> <mn>5</mn> </mtd> <mtd> <mn>8</mn> </mtd> </mtr> <mtr> <mtd> <mn>4</mn> </mtd> <mtd> <mn>8</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>5</mn> </mtd> <mtd> <mn>9</mn> </mtd> <mtd> <mn>2</mn> </mtd> <mtd> <mn>6</mn> </mtd> <mtd> <mn>10</mn> </mtd> <mtd> <mn>3</mn> </mtd> <mtd> <mn>7</mn> </mtd> </mtr> <mtr> <mtd> <mn>5</mn> </mtd> <mtd> <mn>10</mn> </mtd> <mtd> <mn>4</mn> </mtd> <mtd> <mn>9</mn> </mtd> <mtd> <mn>3</mn> </mtd> <mtd> <mn>8</mn> </mtd> <mtd> <mn>2</mn> </mtd> <mtd> <mn>7</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>6</mn> </mtd> </mtr> <mtr> <mtd> <mn>6</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>7</mn> </mtd> <mtd> <mn>2</mn> </mtd> <mtd> <mn>8</mn> </mtd> <mtd> <mn>3</mn> </mtd> <mtd> <mn>9</mn> </mtd> <mtd> <mn>4</mn> </mtd> <mtd> <mn>10</mn> </mtd> <mtd> <mn>5</mn> </mtd> </mtr> <mtr> <mtd> <mn>7</mn> </mtd> <mtd> <mn>3</mn> </mtd> <mtd> <mn>10</mn> </mtd> <mtd> <mn>6</mn> </mtd> <mtd> <mn>2</mn> </mtd> <mtd> <mn>9</mn> </mtd> <mtd> <mn>5</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>8</mn> </mtd> <mtd> <mn>4</mn> </mtd> </mtr> <mtr> <mtd> <mn>8</mn> </mtd> <mtd> <mn>5</mn> </mtd> <mtd> <mn>2</mn> </mtd> <mtd> <mn>10</mn> </mtd> <mtd> <mn>7</mn> </mtd> <mtd> <mn>4</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>9</mn> </mtd> <mtd> <mn>6</mn> </mtd> <mtd> <mn>3</mn> </mtd> </mtr> <mtr> <mtd> <mn>9</mn> </mtd> <mtd> <mn>7</mn> </mtd> <mtd> <mn>5</mn> </mtd> <mtd> <mn>3</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>10</mn> </mtd> <mtd> <mn>8</mn> </mtd> <mtd> <mn>6</mn> </mtd> <mtd> <mn>4</mn> </mtd> <mtd> <mn>2</mn> </mtd> </mtr> <mtr> <mtd> <mn>10</mn> </mtd> <mtd> <mn>9</mn> </mtd> <mtd> <mn>8</mn> </mtd> <mtd> <mn>7</mn> </mtd> <mtd> <mn>6</mn> </mtd> <mtd> <mn>5</mn> </mtd> <mtd> <mn>4</mn> </mtd> <mtd> <mn>3</mn> </mtd> <mtd> <mn>2</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mtable frame="solid" framespacing="0.8em 1.0ex"> <mtr> <mtd> <mtext mathcolor="black">testing </mtext> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> <mtext mathcolor="black"> end.</mtext> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mtable frame="solid" framespacing="0.8em 1.0ex"> <mtr> <mtd> <mtext mathcolor="black">x</mtext> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mtable frame="solid" framespacing="0.8em 1.0ex"> <mtr> <mtd> <mrow> <mi>x</mi> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mtable frame="solid"> <mtr> <mtd> <mtext mathcolor="black">x</mtext> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mtable frame="solid"> <mtr> <mtd> <mrow> <mi>x</mi> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mfrac> <mrow> <mo form="prefix" rspace="0em">ⅆ</mo> <mi>f</mi> </mrow> <mrow> <mo form="prefix" rspace="0em">ⅆ</mo> <mi>x</mi> </mrow> </mfrac> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>5</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo form="prefix" largeop="false" stretchy="false" rspace="0em">∫</mo> <mrow> <mi>x</mi> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.000000em" rspace="0em">ⅆ</mo> <mi>x</mi> </mrow> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mo form="prefix" largeop="false" stretchy="false" lspace="0.277778em" rspace="0em">∬</mo> <mrow> <mi>x</mi> <mo>⁢</mo> <mi>y</mi> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.000000em" rspace="0em">ⅆ</mo> <mi>x</mi> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.000000em" rspace="0em">ⅆ</mo> <mi>y</mi> </mrow> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mo form="prefix" largeop="false" stretchy="false" lspace="0.277778em" rspace="0em">∭</mo> <mrow> <mi>x</mi> <mo>⁢</mo> <mi>y</mi> <mo>⁢</mo> <mi>z</mi> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.000000em" rspace="0em">ⅆ</mo> <mi>x</mi> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.000000em" rspace="0em">ⅆ</mo> <mi>y</mi> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.000000em" rspace="0em">ⅆ</mo> <mi>z</mi> </mrow> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mo form="prefix" largeop="false" stretchy="false" lspace="0.277778em" rspace="0em">⨌</mo> <mrow> <mi>x</mi> <mo>⁢</mo> <mi>y</mi> <mo>⁢</mo> <mi>z</mi> <mo>⁢</mo> <mi>t</mi> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.000000em" rspace="0em">ⅆ</mo> <mi>x</mi> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.000000em" rspace="0em">ⅆ</mo> <mi>y</mi> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.000000em" rspace="0em">ⅆ</mo> <mi>z</mi> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.000000em" rspace="0em">ⅆ</mo> <mi>t</mi> </mrow> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" mathcolor="gray" rspace="0em">mod</mo> <mi>a</mi> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mn>5</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em" mathcolor="gray">mod</mo> <mn>3</mn> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>2</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mn>0</mn> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em" mathcolor="gray">mod</mo> <mn>3</mn> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>1</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mrow> <mrow> <mn>5</mn> <mo>⁢</mo> <mi>x</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mn>4</mn> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">≡</mo> <mn>8</mn> </mrow> <mo lspace="0.444444em">​</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mo form="prefix" mathcolor="gray" rspace="0em">mod</mo> <mn>13</mn> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>a</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mn>5</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>3</mn> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">/</mo> <mn>5</mn> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em" mathcolor="gray">mod</mo> <mn>7</mn> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>6</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mrow> <mn>2</mn> <mo>⁢</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>x</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mn>2</mn> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mrow> <mn>2</mn> <mo>⁢</mo> <mi>x</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mn>1</mn> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em" mathcolor="gray">mod</mo> <mn>3</mn> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mn>2</mn> <mo>⁢</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mtable align="axis" frame="solid" rowlines="solid none" columnlines="solid solid" columnalign="right center left"> <mtr> <mtd> <mo>+</mo> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>000</mn> </mtd> <mtd> <mn>000</mn> </mtd> <mtd> <mn>111</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mn>4. 974 9</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mfrac> <mo form="prefix">ⅆ</mo> <mrow> <mo form="prefix" rspace="0em">ⅆ</mo> <mi>x</mi> </mrow> </mfrac> <mrow> <mi>F</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi>x</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">[</mo> <mrow> <mn>86.333</mn> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mn>146.33</mn> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mn>129.33</mn> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">]</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi mathcolor="gray">BinomialDist</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>x</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">;</mo> <mrow> <mi>n</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>p</mi> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <munderover> <mo form="prefix" movablelimits="true" largeop="false" stretchy="false" lspace="0.277778em" rspace="0em">∑</mo> <mrow> <mi>k</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>0</mn> </mrow> <mi>x</mi> </munderover> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em">(</mo> <mfrac linethickness="0px"> <mi>n</mi> <mi>k</mi> </mfrac> <mo form="postfix" fence="true" stretchy="true" lspace="0em" rspace="0em">)</mo> </mrow> <mo>⁢</mo> <msup> <mi>p</mi> <mi>k</mi> </msup> <mo>⁢</mo> <msup> <mi>q</mi> <mrow> <mi>n</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">−</mo> <mi>k</mi> </mrow> </msup> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo mathcolor="gray" form="prefix" rspace="0em">Pr</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>X</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">≤</mo> <mn>54</mn> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mi mathcolor="gray">BinomialDist</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mn>54</mn> <mo form="infix" lspace="0.000000em" rspace="0.000000em">;</mo> <mrow> <mn>100</mn> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mn>.55</mn> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>.45846</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>k</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mo mathcolor="gray" form="prefix" lspace="0.277778em" rspace="0em">max</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">{</mo> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">|</mo> <mrow> <mfrac> <mrow> <mo form="prefix" rspace="0em">∂</mo> <mi>f</mi> </mrow> <mrow> <mo form="prefix" rspace="0em">∂</mo> <mi>y</mi> </mrow> </mfrac> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>x</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>y</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">|</mo> </mrow> <mo form="infix" lspace="0.166667em" rspace="0.166667em">:</mo> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>x</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>y</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">∈</mo> <mi>D</mi> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">}</mo> </mrow> </mrow> </mrow> <mtext mathcolor="black">.</mtext> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>m</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <munder> <mo mathcolor="gray" form="prefix" movablelimits="false" lspace="0.277778em" rspace="0.166667em">lim</mo> <mrow> <mi>x</mi> <mover> <mo form="infix" lspace="0.000000em" rspace="0.000000em">→</mo> <mrow/> </mover> <mi>a</mi> </mrow> </munder> <mfrac> <mrow> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi>x</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi>a</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> </mrow> <mrow> <mi>x</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mi>a</mi> </mrow> </mfrac> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">|</mo> <mi>A</mi> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">|</mo> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">|</mo> <mtable align="axis" columnalign="left left left left left left"> <mtr> <mtd> <msub> <mi>a</mi> <mrow> <mn>1</mn> <mo>​</mo> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mrow> <mn>1</mn> <mo>​</mo> <mn>2</mn> </mrow> </msub> </mtd> <mtd> <mo form="infix" lspace="mediummathspace" rspace="mediummathspace">⋅</mo> </mtd> <mtd> <mo form="infix" lspace="mediummathspace" rspace="mediummathspace">⋅</mo> </mtd> <mtd> <mo form="infix" lspace="mediummathspace" rspace="mediummathspace">⋅</mo> </mtd> <mtd> <msub> <mi>a</mi> <mrow> <mn>1</mn> <mo>​</mo> <mi>n</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mrow> <mn>2</mn> <mo>​</mo> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mrow> <mn>2</mn> <mo>​</mo> <mn>2</mn> </mrow> </msub> </mtd> <mtd> <mo form="infix" lspace="mediummathspace" rspace="mediummathspace">⋅</mo> </mtd> <mtd> <mo form="infix" lspace="mediummathspace" rspace="mediummathspace">⋅</mo> </mtd> <mtd> <mo form="infix" lspace="mediummathspace" rspace="mediummathspace">⋅</mo> </mtd> <mtd> <msub> <mi>a</mi> <mrow> <mn>2</mn> <mo>​</mo> <mi>n</mi> </mrow> </msub> </mtd> </mtr> <mtr> <mtd> <mo form="infix" lspace="mediummathspace" rspace="mediummathspace">⋅</mo> </mtd> <mtd> <mo form="infix" lspace="mediummathspace" rspace="mediummathspace">⋅</mo> </mtd> <mtd> <mo form="infix" lspace="mediummathspace" rspace="mediummathspace">⋅</mo> </mtd> <mtd> <mspace width="veryverythinmathspace"/> </mtd> <mtd> <mspace width="veryverythinmathspace"/> </mtd> <mtd> <mo form="infix" lspace="mediummathspace" rspace="mediummathspace">⋅</mo> </mtd> </mtr> <mtr> <mtd> <mo form="infix" lspace="mediummathspace" rspace="mediummathspace">⋅</mo> </mtd> <mtd> <mo form="infix" lspace="mediummathspace" rspace="mediummathspace">⋅</mo> </mtd> <mtd> <mspace width="veryverythinmathspace"/> </mtd> <mtd> <mo form="infix" lspace="mediummathspace" rspace="mediummathspace">⋅</mo> </mtd> <mtd> <mspace width="veryverythinmathspace"/> </mtd> <mtd> <mo form="infix" lspace="mediummathspace" rspace="mediummathspace">⋅</mo> </mtd> </mtr> <mtr> <mtd> <mo form="infix" lspace="mediummathspace" rspace="mediummathspace">⋅</mo> </mtd> <mtd> <mo form="infix" lspace="mediummathspace" rspace="mediummathspace">⋅</mo> </mtd> <mtd> <mspace width="veryverythinmathspace"/> </mtd> <mtd> <mspace width="veryverythinmathspace"/> </mtd> <mtd> <mo form="infix" lspace="mediummathspace" rspace="mediummathspace">⋅</mo> </mtd> <mtd> <mo form="infix" lspace="mediummathspace" rspace="mediummathspace">⋅</mo> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mrow> <mi>n</mi> <mo>​</mo> <mn>1</mn> </mrow> </msub> </mtd> <mtd> <msub> <mi>a</mi> <mrow> <mi>n</mi> <mo>​</mo> <mn>2</mn> </mrow> </msub> </mtd> <mtd> <mo form="infix" lspace="mediummathspace" rspace="mediummathspace">⋅</mo> </mtd> <mtd> <mo form="infix" lspace="mediummathspace" rspace="mediummathspace">⋅</mo> </mtd> <mtd> <mo form="infix" lspace="mediummathspace" rspace="mediummathspace">⋅</mo> </mtd> <mtd> <msub> <mi>a</mi> <mrow> <mi>n</mi> <mo>​</mo> <mi>n</mi> </mrow> </msub> </mtd> </mtr> </mtable> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">|</mo> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mrow> <msub> <mi>a</mi> <mrow> <mn>1</mn> <mo>​</mo> <mn>1</mn> </mrow> </msub> <mo>⁢</mo> <msub> <mi>A</mi> <mrow> <mn>1</mn> <mo>​</mo> <mn>1</mn> </mrow> </msub> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <msub> <mi>a</mi> <mrow> <mn>1</mn> <mo>​</mo> <mn>2</mn> </mrow> </msub> <mo>⁢</mo> <msub> <mi>A</mi> <mrow> <mn>1</mn> <mo>​</mo> <mn>2</mn> </mrow> </msub> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>⋯</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <msub> <mi>a</mi> <mrow> <mn>1</mn> <mo>​</mo> <mi>n</mi> </mrow> </msub> <mo>⁢</mo> <msub> <mi>A</mi> <mrow> <mn>1</mn> <mo>​</mo> <mi>n</mi> </mrow> </msub> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>1</mn> </mrow> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mtext mathcolor="green">hl text </mtext> <mrow> <mi>x</mi> </mrow> <mtext mathcolor="black"> end.</mtext> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>1</mn> </mrow> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mtext mathcolor="green">hl to URI </mtext> <mrow> <mi>x</mi> </mrow> <mtext mathcolor="black"> end</mtext> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow id="ht"> <mrow> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>1</mn> </mrow> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mtext mathcolor="green">sex</mtext> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>1</mn> </mrow> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mtext mathcolor="green">jbm</mtext> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr/> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi>x</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo>⁢</mo> <mi>g</mi> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">[</mo> <mi>y</mi> <mo form="postfix" fence="true" stretchy="false">]</mo> </mrow> <mo>⁢</mo> <mi>h</mi> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">{</mo> <mi>z</mi> <mo form="postfix" fence="true" stretchy="false">}</mo> </mrow> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="false">⌊</mo> <mi>a</mi> <mo form="postfix" fence="true" stretchy="false">⌋</mo> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">⌈</mo> <mi>b</mi> <mo form="postfix" fence="true" stretchy="false">⌉</mo> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">〈</mo> <mi>c</mi> <mo form="postfix" fence="true" stretchy="false">〉</mo> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace"/> <mfrac> <mn>123</mn> <mfrac> <mn>456</mn> <mi>A</mi> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">|</mo> </mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">∥</mo> <mfrac> <mi>A</mi> <mfrac> <mi>B</mi> <mi>A</mi> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace"/> </mrow> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">/</mo> <mfrac> <mn>1</mn> <mfrac> <mn>2</mn> <mi>A</mi> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">/</mo> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mfrac> <mn>3</mn> <mfrac> <mn>4</mn> <mi>A</mi> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">↕</mo> <mfrac> <mn>5</mn> <mfrac> <mn>6</mn> <mi>A</mi> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">↕</mo> </mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace"/> <mfrac> <mn>7</mn> <mfrac> <mn>8</mn> <mi>A</mi> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace"/> </mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">⇕</mo> <mfrac> <mfrac> <mn>9</mn> <mn>20</mn> </mfrac> <mfrac> <mn>10</mn> <mi>A</mi> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">⇕</mo> </mrow> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">↑</mo> <mfrac> <mn>11</mn> <mfrac> <mn>12</mn> <mi>A</mi> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">↑</mo> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">⇑</mo> <mfrac> <mn>13</mn> <mfrac> <mn>14</mn> <mi>A</mi> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">⇑</mo> </mrow> </mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">↓</mo> <mfrac> <mn>15</mn> <mfrac> <mn>16</mn> <mi>A</mi> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">↓</mo> </mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">⇓</mo> <mfrac> <mn>17</mn> <mfrac> <mn>18</mn> <mi>A</mi> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">⇓</mo> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>x</mi> <mo>⁢</mo> <mtable align="axis" columnalign="left left"> <mtr> <mtd> <mrow> <mi>x</mi> </mrow> </mtd> <mtd> <mrow> <mi>x</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>x</mi> </mrow> </mtd> <mtd> <mrow> <mi>x</mi> </mrow> </mtd> </mtr> </mtable> <mo>⁢</mo> <mi>x</mi> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>…</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <msub> <mi>a</mi> <mi>n</mi> </msub> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">⋅</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <msub> <mi>b</mi> <mn>1</mn> </msub> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <msub> <mi>b</mi> <mn>2</mn> </msub> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>…</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <msub> <mi>b</mi> <mi>n</mi> </msub> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>⁢</mo> <msubsup> <mi>b</mi> <mn>1</mn> <mo form="infix" lspace="mediummathspace" rspace="mediummathspace">*</mo> </msubsup> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <msub> <mi>a</mi> <mn>2</mn> </msub> <mo>⁢</mo> <msubsup> <mi>b</mi> <mn>2</mn> <mo form="infix" lspace="mediummathspace" rspace="mediummathspace">*</mo> </msubsup> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>⋯</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <msub> <mi>a</mi> <mi>n</mi> </msub> <mo>⁢</mo> <msubsup> <mi>b</mi> <mi>n</mi> <mo form="infix" lspace="mediummathspace" rspace="mediummathspace">*</mo> </msubsup> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">⌊</mo> <mfrac> <mi>n</mi> <mn>5</mn> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">⌋</mo> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">⌊</mo> <mfrac> <mi>n</mi> <msup> <mn>5</mn> <mn>2</mn> </msup> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">⌋</mo> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">⌊</mo> <mfrac> <mi>n</mi> <msup> <mn>5</mn> <mn>3</mn> </msup> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">⌋</mo> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">⌊</mo> <mfrac> <mi>n</mi> <msup> <mn>5</mn> <mn>4</mn> </msup> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">⌋</mo> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>⋯</mi> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>⋯</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <munder> <munder> <mrow> <mi>x</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>⋯</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>x</mi> </mrow> <mo stretchy="true">︸</mo> </munder> <mrow> <mi>k</mi> <mtext mathcolor="black"> times</mtext> </mrow> </munder> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mroot> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>⁢</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo>⁢</mo> <mi>⋯</mi> <mo>⁢</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> </mrow> <mi>n</mi> </mroot> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>n</mi> <mo form="postfix" lspace="0em" rspace="0.277778em">!</mo> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mn>1</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">×</mo> <mn>2</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">×</mo> <mn>3</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">×</mo> <mn>4</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">×</mo> <mi>⋯</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">×</mo> <mi>n</mi> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>P</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">:</mo> <mrow> <mi>a</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <msub> <mi>x</mi> <mn>0</mn> </msub> <mo form="infix" lspace="0.277778em" rspace="0.277778em"><</mo> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo form="infix" lspace="0.277778em" rspace="0.277778em"><</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> <mo form="infix" lspace="0.277778em" rspace="0.277778em"><</mo> <mi>⋯</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em"><</mo> <msub> <mi>x</mi> <mi>n</mi> </msub> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mi>b</mi> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi>x</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mfrac> <mn>30</mn> <mrow> <mn>13</mn> <mo>⁢</mo> <mrow> <mi mathcolor="gray">cos</mi> <mo rspace="0.166667em">⁡</mo> <mi>x</mi> </mrow> </mrow> </mfrac> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mfrac> <mn>10</mn> <mn>3</mn> </mfrac> <mo>⁢</mo> <msqrt> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mn>100</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mfrac> <mn>9</mn> <mrow> <msup> <mi mathcolor="gray">cos</mi> <mn>2</mn> </msup> <mo rspace="0.166667em">⁡</mo> <mi>x</mi> </mrow> </mfrac> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mfrac> <mn>60</mn> <mrow> <mi mathcolor="gray">cos</mi> <mo rspace="0.166667em">⁡</mo> <mi>x</mi> </mrow> </mfrac> <mo>⁢</mo> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mi>x</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mfrac> <mn>29</mn> <mn>90</mn> </mfrac> <mo>⁢</mo> <mi>π</mi> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </msqrt> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mrow> <mo form="prefix" largeop="false" stretchy="true" maxsize="1.4" minsize="1.4" rspace="0em">∫</mo> <mrow> <mrow> <mi mathcolor="gray">cos</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>A</mi> <mo>⁢</mo> <mi>x</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo>⁢</mo> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>B</mi> <mo>⁢</mo> <mi>x</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.166667em" rspace="0em">ⅆ</mo> <mi>x</mi> </mrow> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mfrac> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mrow> <mi mathcolor="gray">cos</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>B</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mi>A</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> <mo>⁢</mo> <mi>x</mi> </mrow> </mrow> </mrow> <mrow> <mn>2</mn> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>B</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mi>A</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> </mfrac> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mfrac> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mrow> <mi mathcolor="gray">cos</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>B</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>A</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> <mo>⁢</mo> <mi>x</mi> </mrow> </mrow> </mrow> <mrow> <mn>2</mn> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>B</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>A</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> </mfrac> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>C</mi> </mrow> </mrow> <mtext mathcolor="black"> .</mtext> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mn>235.3</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mn>813</mn> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>1048. 3</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <munder> <mo mathcolor="gray" form="prefix" movablelimits="true" rspace="0.166667em">max</mo> <mrow> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>2</mn> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">≤</mo> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">≤</mo> <mn>2</mn> </mrow> </munder> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <msup> <mi>x</mi> <mn>3</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>6</mn> <mo>⁢</mo> <mi>x</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mn>3</mn> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>8.0</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>x</mi> <mo>⁢</mo> <mi mathcolor="gray">decade</mi> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mn>2</mn> <mo>⁢</mo> <mi mathcolor="gray">century</mi> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mfrac> <mrow> <msup> <mo form="prefix" rspace="0em">ⅆ</mo> <mn>5</mn> </msup> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <msup> <mi>x</mi> <mn>7</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>3</mn> <mo>⁢</mo> <msup> <mi>x</mi> <mn>6</mn> </msup> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mrow> <mo form="prefix" rspace="0em">ⅆ</mo> <msup> <mi>x</mi> <mn>5</mn> </msup> </mrow> </mfrac> <mtext mathcolor="black">  </mtext> <mfrac> <mrow> <msup> <mo form="prefix" rspace="0em">ⅆ</mo> <mi>n</mi> </msup> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>x</mi> </mrow> </mrow> <mrow> <mo form="prefix" rspace="0em">ⅆ</mo> <msup> <mi>x</mi> <mi>n</mi> </msup> </mrow> </mfrac> <mtext mathcolor="black">  </mtext> <mrow> <mfrac> <msup> <mo form="prefix" rspace="0em">ⅆ</mo> <mn>3</mn> </msup> <mrow> <mo form="prefix" rspace="0em">ⅆ</mo> <msup> <mi>x</mi> <mn>3</mn> </msup> </mrow> </mfrac> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi>x</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> </mrow> <mtext mathcolor="black">  </mtext> <mrow> <mfrac> <msup> <mo form="prefix" rspace="0em">ⅆ</mo> <mn>2</mn> </msup> <mrow> <mo form="prefix" rspace="0em">ⅆ</mo> <msup> <mi>t</mi> <mn>2</mn> </msup> </mrow> </mfrac> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mrow> <mn>4</mn> <mo>⁢</mo> <msup> <mi>t</mi> <mn>5</mn> </msup> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>3</mn> <mo>⁢</mo> <mi>t</mi> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi>x</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mfrac> <mn>30</mn> <mrow> <mn>13</mn> <mo>⁢</mo> <mrow> <mi mathcolor="gray">cos</mi> <mo rspace="0.166667em">⁡</mo> <mi>x</mi> </mrow> </mrow> </mfrac> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mfrac> <mn>10</mn> <mn>3</mn> </mfrac> <mo>⁢</mo> <msqrt> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mn>100</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mfrac> <mn>9</mn> <mrow> <msup> <mi mathcolor="gray">cos</mi> <mn>2</mn> </msup> <mo rspace="0.166667em">⁡</mo> <mi>x</mi> </mrow> </mfrac> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mfrac> <mn>60</mn> <mrow> <mi mathcolor="gray">cos</mi> <mo rspace="0.166667em">⁡</mo> <mi>x</mi> </mrow> </mfrac> <mo>⁢</mo> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mi>x</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mfrac> <mn>29</mn> <mn>90</mn> </mfrac> <mo>⁢</mo> <mi>π</mi> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </msqrt> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <msub> <mo form="prefix" largeop="false" stretchy="true" maxsize="1.4" minsize="1.4" rspace="0em">∫</mo> <msup> <mi mathvariant="bold">R</mi> <mn>3</mn> </msup> </msub> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mfrac> <mrow> <msup> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">|</mo> <msub> <mi>u</mi> <mn>1</mn> </msub> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">|</mo> </mrow> <mn>2</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <msup> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">|</mo> <mrow> <mo form="prefix" rspace="0em">∇</mo> <msub> <mi>u</mi> <mn>0</mn> </msub> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">|</mo> </mrow> <mn>2</mn> </msup> </mrow> <mn>2</mn> </mfrac> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mfrac> <msup> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">|</mo> <msub> <mi>u</mi> <mn>0</mn> </msub> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">|</mo> </mrow> <mn>6</mn> </msup> <mn>6</mn> </mfrac> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.166667em" rspace="0em">ⅆ</mo> <mi>x</mi> </mrow> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em"><</mo> <mi>∞</mi> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mo form="prefix" rspace="0em">∇×</mo> <mi mathvariant="bold">F</mi> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">⋅</mo> <mi mathvariant="bold">k</mi> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mi>z</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mn>1</mn> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>M</mi> <mo>⁢</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <msup> <mi>M</mi> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mi>M</mi> <mi>M</mi> </mfrac> </mstyle> </mrow> </msup> <mi>M</mi> </mfrac> </mstyle> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <msub> <mo form="prefix" rspace="0em">ⅅ</mo> <mi>x</mi> </msub> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> <mtext>  </mtext> <mrow> <msub> <mo form="prefix" lspace="0.000000em" rspace="0em">ⅅ</mo> <mi>x</mi> </msub> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mtext>  </mtext> <mrow> <msub> <mo form="prefix" lspace="0.166667em" rspace="0em">ⅅ</mo> <mrow> <mi>x</mi> <mo>​</mo> <mi>x</mi> </mrow> </msub> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mtext>  </mtext> <mrow> <msub> <mo form="prefix" lspace="0.166667em" rspace="0em">ⅅ</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> </msub> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mtext>  </mtext> <mrow> <msub> <mo form="prefix" lspace="0.166667em" rspace="0em">ⅅ</mo> <mrow> <mi>x</mi> <mo>​</mo> <mi>y</mi> </mrow> </msub> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>⁢</mo> <msup> <mi>y</mi> <mn>3</mn> </msup> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> <mtext>  </mtext> <mrow> <msub> <mo form="prefix" lspace="0.166667em" rspace="0em">ⅅ</mo> <mrow> <msup> <mi>x</mi> <mi>s</mi> </msup> <mo>​</mo> <msup> <mi>y</mi> <mi>t</mi> </msup> </mrow> </msub> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>⁢</mo> <msup> <mi>y</mi> <mn>3</mn> </msup> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mn>5</mn> <mspace width="0.500000in"/> <mrow> <mn>24</mn> <mo form="postfix" lspace="0em" rspace="0.000000em">!</mo> </mrow> <mspace width="0.500000in"/> <msup> <mi>x</mi> <mn>6</mn> </msup> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mtable frame="solid"> <mtr> <mtd> <mpadded depth="1.500000in" height="1.500000in"> <mrow> <mtable align="axis"> <mtr> <mtd> <mrow> <mi>x</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mroot> <mfrac> <msup> <mi>a</mi> <mpadded depth="0.100000in" height="0.200000in"> <mrow> <mi>y</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">−</mo> <mn>1</mn> </mrow> </mpadded> </msup> <mpadded depth="+3.5pt" height="+8.5pt"> <mn>12.34</mn> </mpadded> </mfrac> <mpadded depth="0.300000in" height="0.300000in"> <mn>2</mn> </mpadded> </mroot> </mrow> </mtd> <mtd> <mpadded depth="0.300000in" height="0.300000in"> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> </mpadded> </mtd> </mtr> <mtr> <mtd> <mpadded depth="+3.5pt" height="+8.5pt"> <mspace width="veryverythinmathspace"/> </mpadded> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> </mtable> </mrow> </mpadded> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mtable align="axis" rowlines="solid" columnalign="center"> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="0em" rspace="0em">(</mo> <mtable align="axis" columnalign="center"> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mi>i</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mi>i</mi> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> </mtable> <mo form="postfix" fence="true" stretchy="true" symmetric="true" lspace="0em" rspace="0em">)</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="0em" rspace="0em">[</mo> <mtable align="axis" columnalign="center"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>1</mn> </mrow> </mtd> </mtr> </mtable> <mo form="postfix" fence="true" stretchy="true" symmetric="true" lspace="0em" rspace="0em">]</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="0em" rspace="0em">|</mo> <mtable align="axis" columnalign="center"> <mtr> <mtd> <mi>a</mi> </mtd> <mtd> <mi>b</mi> </mtd> </mtr> <mtr> <mtd> <mi>c</mi> </mtd> <mtd> <mi>d</mi> </mtd> </mtr> </mtable> <mo form="postfix" fence="true" stretchy="true" symmetric="true" lspace="0em" rspace="0em">|</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="0em" rspace="0em">∥</mo> <mtable align="axis" columnalign="center"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>0</mn> </mtd> <mtd> <mn>1</mn> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mn>11</mn> </mtd> <mtd> <mspace width="veryverythinmathspace"/> </mtd> </mtr> </mtable> <mo form="postfix" fence="true" stretchy="true" symmetric="true" lspace="0em" rspace="0em">∥</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mstyle scriptlevel="+1"> <mtable align="axis" columnalign="center"> <mtr> <mtd> <mn>1</mn> </mtd> <mtd> <mn>2</mn> </mtd> <mtd> <mn>3</mn> </mtd> </mtr> <mtr> <mtd> <mn>4</mn> </mtd> <mtd> <mn>5</mn> </mtd> <mtd> <mspace width="veryverythinmathspace"/> </mtd> </mtr> </mtable> </mstyle> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mtext mathcolor="black">testing </mtext> <mtable frame="solid"> <mtr> <mtd> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mover> <mi>a</mi> <mo form="postfix" accent="true">̂</mo> </mover> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mover> <mi>b</mi> <mo form="postfix" accent="true">ˇ</mo> </mover> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mover> <mi>c</mi> <mo form="postfix" accent="true">˜</mo> </mover> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mover> <mi>d</mi> <mo form="postfix" accent="true">´</mo> </mover> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mover> <mi>e</mi> <mo form="postfix" accent="true">`</mo> </mover> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mover> <mi>f</mi> <mo form="postfix" accent="true">˘</mo> </mover> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mover> <mi>g</mi> <mo form="postfix" accent="true">¯</mo> </mover> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>h</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mover> <mi>i</mi> <mo form="postfix" accent="true">˚</mo> </mover> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mover> <mi>j</mi> <mo form="postfix" accent="true">˙</mo> </mover> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mover> <mi>k</mi> <mo form="postfix" accent="true">¨</mo> </mover> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mover> <mi>l</mi> <mo form="postfix" accent="true">⃛</mo> </mover> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mover> <mi>m</mi> <mo form="postfix" accent="true">⃜</mo> </mover> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mover> <mi>n</mi> <mo form="postfix" accent="true">→</mo> </mover> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>f</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>g</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mi>x</mi> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mrow> <msup> <mi mathcolor="gray">sin</mi> <mn>3</mn> </msup> <mo rspace="0.166667em">⁡</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> <mo>⁢</mo> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <maction actiontype="toggle" selection="2"> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mn>12</mn> </mrow> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mn>12</mn> </mrow> </maction> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mn>1234</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mtable align="axis" columnalign="left left left left"> <mtr> <mtd columnspan="2" columnalign="left"> <mrow> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>1</mn> </mrow> </mtd> <mtd> <mtext mathcolor="black">not</mtext> </mtd> <mtd> <mtext mathcolor="black">here</mtext> </mtd> </mtr> <mtr> <mtd> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> </mrow> </mtd> <mtd columnspan="2" columnalign="left"> <mtext mathcolor="black">merged</mtext> </mtd> <mtd> <mrow> <msub> <mi>y</mi> <mn>1</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mtext mathcolor="black">jbm</mtext> </mtd> <mtd> <mtext mathcolor="black">lowlife</mtext> </mtd> <mtd columnspan="2" columnalign="left"> <mtext mathcolor="black">The end.</mtext> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <msup> <mi>z</mi> <mn>2</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>1</mn> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" mathbackground="transparent"> <mtable> <mtr> <mtd groupalign="right left"> <maligngroup/> <mrow> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> </mrow> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <msup> <mi>z</mi> <mn>2</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>1</mn> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd groupalign="right left"> <maligngroup/> <mrow> <mrow> <mi>x</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <msup> <mi>y</mi> <mn>3</mn> </msup> </mrow> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <msup> <mi>z</mi> <mn>3</mn> </msup> </mrow> </mtd> </mtr> </mtable> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" mathbackground="transparent"> <mtable> <mtr> <mtd groupalign="right center left"> <maligngroup/> <mrow> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> </mrow> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <maligngroup/> <mrow> <msup> <mi>z</mi> <mn>2</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>1</mn> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd groupalign="right center left"> <maligngroup/> <mrow> <mrow> <mi>x</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <msup> <mi>y</mi> <mn>3</mn> </msup> </mrow> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <maligngroup/> <msup> <mi>z</mi> <mn>3</mn> </msup> </mrow> </mtd> </mtr> </mtable> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" mathbackground="transparent"> <mtable> <mtr> <mtd groupalign="right left"> <maligngroup/> <mrow> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> </mrow> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd groupalign="right left"> <maligngroup/> <mrow> <mi>x</mi> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <msqrt> <mrow> <mn>1</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> </mtd> </mtr> </mtable> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" mathbackground="transparent"> <mtable> <mtr> <mtd groupalign="center"> <maligngroup/> <mrow> <msup> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>a</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>b</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> <mn>2</mn> </msup> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <msup> <mi>a</mi> <mn>2</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>2</mn> <mo>⁢</mo> <mi>a</mi> <mo>⁢</mo> <mi>b</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <msup> <mi>b</mi> <mn>2</mn> </msup> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd groupalign="center"> <maligngroup/> <mrow> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>a</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>b</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">⋅</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>a</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mi>b</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <msup> <mi>a</mi> <mn>2</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <msup> <mi>b</mi> <mn>2</mn> </msup> </mrow> </mrow> </mtd> </mtr> </mtable> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" mathbackground="transparent"> <mtable> <mtr> <mtd groupalign="right"> <maligngroup/> <mtext mathcolor="black">First line of equation</mtext> </mtd> </mtr> <mtr> <mtd groupalign="center"> <maligngroup/> <mtext mathcolor="black">Middle line of equation</mtext> </mtd> </mtr> <mtr> <mtd groupalign="center"> <maligngroup/> <mtext mathcolor="black">Other middle line of equation</mtext> </mtd> </mtr> <mtr> <mtd groupalign="center"> <maligngroup/> <mtext mathcolor="black">Last line of equation</mtext> </mtd> </mtr> </mtable> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" mathbackground="transparent"> <mtable> <mtr> <mtd groupalign="right left right left right left"> <maligngroup/> <mrow> <msub> <mi>L</mi> <mn>1</mn> </msub> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <msub> <mi>R</mi> <mn>1</mn> </msub> </mrow> <maligngroup/> <mtext>  </mtext> <mrow> <msub> <mi>L</mi> <mn>2</mn> </msub> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <msub> <mi>R</mi> <mn>2</mn> </msub> </mrow> </mtd> </mtr> <mtr> <mtd groupalign="right left right left right left"> <maligngroup/> <mrow> <msub> <mi>L</mi> <mn>3</mn> </msub> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <msub> <mi>R</mi> <mn>3</mn> </msub> </mrow> <maligngroup/> <mtext>  </mtext> <mrow> <msub> <mi>L</mi> <mn>4</mn> </msub> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <msub> <mi>R</mi> <mn>4</mn> </msub> </mrow> </mtd> </mtr> </mtable> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mtable> <mtr> <mtd groupalign="right left"> <maligngroup/> <mrow> <msup> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>a</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>b</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> <mn>4</mn> </msup> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <msup> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>a</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>b</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> <mn>2</mn> </msup> <mo>⁢</mo> <msup> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>a</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>b</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd groupalign="right left"> <maligngroup/> <maligngroup/> <mo form="infix" lspace="thickmathspace" rspace="0.277778em">=</mo> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <msup> <mi>a</mi> <mn>2</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>2</mn> <mo>⁢</mo> <mi>a</mi> <mo>⁢</mo> <mi>b</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <msup> <mi>b</mi> <mn>2</mn> </msup> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <msup> <mi>a</mi> <mn>2</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>2</mn> <mo>⁢</mo> <mi>a</mi> <mo>⁢</mo> <mi>b</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <msup> <mi>b</mi> <mn>2</mn> </msup> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd groupalign="right left"> <maligngroup/> <maligngroup/> <mo form="infix" lspace="thickmathspace" rspace="0.277778em">=</mo> <mrow> <msup> <mi>a</mi> <mn>4</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>4</mn> <mo>⁢</mo> <msup> <mi>a</mi> <mn>3</mn> </msup> <mo>⁢</mo> <mi>b</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>6</mn> <mo>⁢</mo> <msup> <mi>a</mi> <mn>2</mn> </msup> <mo>⁢</mo> <msup> <mi>b</mi> <mn>2</mn> </msup> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>4</mn> <mo>⁢</mo> <mi>a</mi> <mo>⁢</mo> <msup> <mi>b</mi> <mn>3</mn> </msup> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <msup> <mi>b</mi> <mn>4</mn> </msup> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mtable> <mtr> <mtd groupalign="right left"> <maligngroup/> <mrow> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> </mrow> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mn>1</mn> </mrow> </mtd> </mtr> <mtr> <mtd groupalign="right left"> <maligngroup/> <mrow> <mi>x</mi> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <msqrt> <mrow> <mn>1</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <msup> <mi>y</mi> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> </mtd> </mtr> </mtable> <mtext>  </mtext> <mtable> <mtr> <mtd groupalign="center"> <maligngroup/> <mrow> <msup> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>a</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>b</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> <mn>2</mn> </msup> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <msup> <mi>a</mi> <mn>2</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>2</mn> <mo>⁢</mo> <mi>a</mi> <mo>⁢</mo> <mi>b</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <msup> <mi>b</mi> <mn>2</mn> </msup> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd groupalign="center"> <maligngroup/> <mrow> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>a</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>b</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">⋅</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mi>a</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mi>b</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <msup> <mi>a</mi> <mn>2</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <msup> <mi>b</mi> <mn>2</mn> </msup> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mtable align="axis" columnalign="left left"> <mtr> <mtd> <mstyle fontweight="bold"> <mtext mathcolor="black">Vertex</mtext> </mstyle> </mtd> <mtd> <mrow> <mi>V</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mn>0</mn> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mn>0</mn> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mstyle fontweight="bold"> <mtext mathcolor="black">Focus</mtext> </mstyle> </mtd> <mtd> <mrow> <mi>F</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <mn>0</mn> <mo form="infix" lspace="0.000000em" rspace="0.000000em">,</mo> <mi>p</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mstyle fontweight="bold"> <mtext mathcolor="black">Directrix</mtext> </mstyle> </mtd> <mtd> <mrow> <mi>y</mi> <mo form="infix" lspace="0.277778em" rspace="thickmathspace">=</mo> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mi>p</mi> </mrow> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mo form="prefix">ⅆ</mo> <mrow> <mo form="prefix" rspace="0em">ⅆ</mo> <mi>x</mi> </mrow> </mfrac> </mstyle> </mrow> <mtext>  </mtext> <mrow> <mo form="prefix" fence="true" stretchy="false">(</mo> <mrow> <msup> <mi mathcolor="gray">csc</mi> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>1</mn> </mrow> </msup> <mo rspace="0.166667em">⁡</mo> <mi>x</mi> </mrow> <mo form="postfix" fence="true" stretchy="false">)</mo> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="thickmathspace">=</mo> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>1</mn> <mrow> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">|</mo> <mi>x</mi> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">|</mo> </mrow> <mo>⁢</mo> <msqrt> <mrow> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>1</mn> </mrow> </msqrt> </mrow> </mfrac> </mstyle> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mrow> <msup> <mi mathcolor="gray">tanh</mi> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mn>1</mn> </mrow> </msup> <mo rspace="0.166667em">⁡</mo> <mi>x</mi> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mrow> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mstyle> </mrow> <mo>⁢</mo> <mrow> <mi mathcolor="gray">ln</mi> <mo rspace="0.166667em">⁡</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <mn>1</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>x</mi> </mrow> <mrow> <mn>1</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mi>x</mi> </mrow> </mfrac> </mstyle> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mrow> </mrow> </mrow> <mtext>  </mtext> <mrow> <mrow> <mo form="prefix" lspace="0.222222em" rspace="0em">−</mo> <mn>1</mn> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em"><</mo> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em"><</mo> <mn>1</mn> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mrow> <mi>∠</mi> <mi>α</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mi>∠</mi> <mi>A</mi> <mi>B</mi> <mi>C</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mi>∠</mi> <mn>1</mn> </mrow> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mi>▵</mi> <mi>a</mi> <mi>b</mi> <mi>c</mi> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>y</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <msup> <mi>e</mi> <mrow> <mo form="prefix" lspace="mediummathspace" rspace="0em">−</mo> <mrow> <mo form="prefix" largeop="false" stretchy="false" lspace="0.000000em" rspace="0em">∫</mo> <mrow> <mi>P</mi> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.000000em" rspace="0em">ⅆ</mo> <mi>x</mi> </mrow> </mrow> </mrow> </mrow> </msup> <mo>⁢</mo> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">[</mo> <mrow> <mrow> <mo form="prefix" largeop="false" stretchy="false" rspace="0em">∫</mo> <mrow> <msup> <mi>e</mi> <mrow> <mo form="prefix" largeop="false" stretchy="false" rspace="0em">∫</mo> <mrow> <mi>P</mi> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.000000em" rspace="0em">ⅆ</mo> <mi>x</mi> </mrow> </mrow> </mrow> </msup> <mo>⁢</mo> <mi>Q</mi> <mo>⁢</mo> <mrow> <mo form="prefix" lspace="0.000000em" rspace="0em">ⅆ</mo> <mi>x</mi> </mrow> </mrow> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>c</mi> </mrow> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">]</mo> </mrow> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mn>1</mn> <mrow> <mstyle mathsize="2.50ex"> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> </mstyle> </mrow> <msup> <mrow> <mstyle mathsize="2.50ex"> <mi>y</mi> </mstyle> </mrow> <mn>3</mn> </msup> </mrow> </mrow> </mstyle> </mrow> </mtd> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mstyle mathsize="2.50ex"> <mrow> <mi>x</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <mrow> <mn>1</mn> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>y</mi> </mrow> </mrow> </mstyle> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mo form="prefix" rspace="0em">$</mo> <mn>1.00</mn> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>25</mn> <mo form="postfix" lspace="0em" rspace="0.222222em">¢</mo> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>3</mn> <mo form="postfix" lspace="0em" rspace="0.222222em">£</mo> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>2.45</mn> <mo form="postfix" lspace="0em" rspace="0.222222em">¤</mo> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>0.7</mn> <mo form="postfix" lspace="0em" rspace="0.222222em">¥</mo> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mi>a</mi> <mo form="postfix" lspace="0em" rspace="0.222222em">₠</mo> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>20</mn> <mo form="postfix" lspace="0em" rspace="0.222222em">₣</mo> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mn>30</mn> <mo form="postfix" lspace="0em" rspace="0.222222em">₤</mo> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>4.56</mn> <mo form="postfix" lspace="0em">₧</mo> </mrow> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" mathbackground="transparent"> <mtable rowspacing="2.000000ex 3.000000ex 1.500000ex "> <mtr> <mtd groupalign="right center left"> <maligngroup/> <mrow> <mrow> <mrow> <mn>2</mn> <mo>⁢</mo> <mi>x</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>y</mi> </mrow> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <maligngroup/> <mn>3</mn> </mrow> </mtd> </mtr> <mtr> <mtd groupalign="right center left"> <maligngroup/> <mrow> <mrow> <mrow> <mn>3</mn> <mo>⁢</mo> <mi>x</mi> </mrow> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mrow> <mn>4</mn> <mo>⁢</mo> <mi>y</mi> </mrow> </mrow> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <maligngroup/> <mn>5</mn> </mrow> </mtd> </mtr> <mtr> <mtd groupalign="right center left"> <maligngroup/> <mrow> <mrow> <mi>a</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>b</mi> </mrow> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <maligngroup/> <mrow> <mi>c</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mn>12345</mn> </mrow> </mrow> </mtd> </mtr> </mtable> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mtable align="axis"> <mtr> <mtd> <mstyle fontweight="bold"> <mtext mathcolor="black">Unrestricted</mtext> </mstyle> </mtd> <mtd> <mtext mathcolor="black">   </mtext> </mtd> <mtd> <mstyle fontweight="bold"> <mtext mathcolor="black">Symmetric</mtext> </mstyle> </mtd> <mtd> <mtext mathcolor="black"> </mtext> </mtd> <mtd> <mstyle fontweight="bold"> <mtext mathcolor="black">Antisymmetric</mtext> </mstyle> </mtd> <mtd> <mtext mathcolor="black">  </mtext> </mtd> <mtd> <mstyle fontweight="bold"> <mtext mathcolor="black">Triangular</mtext> </mstyle> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>a</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">≠</mo> <mi>b</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">≠</mo> <mi>x</mi> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>c</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">≮</mo> <mi>d</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">≮</mo> <mi>y</mi> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>e</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">≯</mo> <mi>f</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">≯</mo> <mn>11</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>g</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">∉</mo> <mi>h</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">∉</mo> <mi>Z</mi> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>k</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">≁</mo> <mi>l</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">≁</mo> <mn>3</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mrow> <mi>A</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">⊄</mo> <mi>B</mi> </mrow> <mo form="infix" lspace="0.277778em" rspace="0.277778em">⊂</mo> <mi>C</mi> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>A</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">⊈</mo> <mi>B</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">⊈</mo> <mi>C</mi> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mn>10</mn> <mo form="infix" lspace="0.000000em" rspace="0.000000em">≢</mo> <mn>11</mn> <mo form="infix" lspace="0.277778em" rspace="0.277778em">≡</mo> <mn>12</mn> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>x</mi> <mo form="infix" lspace="0.000000em" rspace="0.000000em">≰⃥</mo> <mi>y</mi> <mo form="infix" lspace="0.277778em" rspace="0.277778em">≰⃥</mo> <mi>z</mi> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mover> <mi mathcolor="gray">lim</mi> <mo stretchy="true" accent="true">¯</mo> </mover> <mi>x</mi> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <munder> <mi mathcolor="gray">lim</mi> <mo stretchy="true" accent="true">̲</mo> </munder> <mi>x</mi> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <munder> <mi mathcolor="gray">lim</mi> <mo stretchy="true" accent="true">→</mo> </munder> <mi>x</mi> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <munder> <mi mathcolor="gray">lim</mi> <mo stretchy="true" accent="true">←</mo> </munder> <mi>x</mi> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" mathbackground="transparent"> <mtable> <mtr> <mtd groupalign="right center left"> <maligngroup/> <mrow> <mi>x</mi> <maligngroup/> <mo form="infix" lspace="0.277778em" rspace="0.277778em">=</mo> <maligngroup/> <mrow> <mi>y</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>z</mi> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd groupalign="right center left"> <maligngroup/> <maligngroup/> <mo form="infix" lspace="thickmathspace" rspace="0.277778em">=</mo> <maligngroup/> <mrow> <mi>k</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>m</mi> </mrow> </mtd> </mtr> </mtable> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mtable align="axis" columnalign="left"> <mtr> <mtd> <mstyle mathsize="2.00ex"> <mtext mathcolor="black">College Algebra </mtext> </mstyle> <mtext mathcolor="black">Second Edition</mtext> </mtd> </mtr> <mtr> <mtd> <mstyle mathsize="2.00ex"> <mtext mathcolor="black">James Stewart </mtext> </mstyle> <mtext mathcolor="black">McMaster Universitiy</mtext> </mtd> </mtr> <mtr> <mtd> <mstyle mathsize="2.00ex"> <mtext mathcolor="black">Lothar Redlin</mtext> </mstyle> <mtext mathcolor="black"> Pennsylvania State University</mtext> </mtd> </mtr> <mtr> <mtd> <mstyle mathsize="2.00ex"> <mtext mathcolor="black">Saleem Watson</mtext> </mstyle> <mtext mathcolor="black"> California State University, Long Beach</mtext> </mtd> </mtr> <mtr> <mtd> <mtext mathcolor="black">Copyright 1996, ISBN 0 534-33983-2</mtext> </mtd> </mtr> <mtr> <mtd> <mtext mathcolor="black">Brooks/Cole Publishing Company</mtext> </mtd> </mtr> <mtr> <mtd> <mtext mathcolor="black">An International Thomson Publishing Company</mtext> </mtd> </mtr> </mtable> <mspace width="thickmathspace"/> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo stretchy="true" minsize="1.2" maxsize="1.2" form="prefix" fence="true">{</mo> <mrow> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo stretchy="true" minsize="1.2" maxsize="1.2" lspace="0.222222em" rspace="0.222222em">↑</mo> <munderover> <mo form="prefix" movablelimits="true" largeop="false" stretchy="false" lspace="0.222222em" rspace="0em">∑</mo> <mn>1</mn> <mn>2</mn> </munderover> </mrow> <mo stretchy="true" minsize="1.2" maxsize="1.2" form="postfix" fence="true">}</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo stretchy="true" minsize="1.8" maxsize="1.8" form="prefix" fence="true">〈</mo> <mrow> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo stretchy="true" minsize="1.8" maxsize="1.8" lspace="0.222222em" rspace="0.222222em">|</mo> <munderover> <mo form="prefix" movablelimits="true" largeop="false" stretchy="false" lspace="0.222222em" rspace="0em">∑</mo> <mn>1</mn> <mn>2</mn> </munderover> </mrow> <mo stretchy="true" minsize="1.8" maxsize="1.8" form="postfix" fence="true">〉</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo stretchy="true" minsize="2.4" maxsize="2.4" form="prefix" fence="true">⌈</mo> <mrow> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo stretchy="true" minsize="2.4" maxsize="2.4" lspace="0.222222em" rspace="0.555556em">|</mo> <munderover> <mo form="prefix" movablelimits="true" largeop="false" stretchy="false" lspace="0.222222em" rspace="0em">∑</mo> <mn>1</mn> <mn>2</mn> </munderover> </mrow> <mo stretchy="true" minsize="2.4" maxsize="2.4" form="postfix" fence="true">⌉</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo stretchy="true" minsize="3.0" maxsize="3.0" form="prefix" fence="true">⇓</mo> <mrow> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo stretchy="true" minsize="3.0" maxsize="3.0" lspace="0.222222em" rspace="0.222222em">↕</mo> <munderover> <mo form="prefix" movablelimits="true" largeop="false" stretchy="false" lspace="0.222222em" rspace="0em">∑</mo> <mn>1</mn> <mn>2</mn> </munderover> </mrow> <mo stretchy="true" minsize="3.0" maxsize="3.0" form="postfix" fence="true">⇓</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">[</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">]</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">(</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">)</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">{</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">}</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">〈</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">〉</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">⌊</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">⌋</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">⌈</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">⌉</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">↑</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">↑</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">↓</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">↓</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">↕</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">↕</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">⇑</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">⇑</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">⇓</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">⇓</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">⇕</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">⇕</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace"/> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace"/> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">\arrowvert</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">\arrowvert</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">\Arrowvert</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">\Arrowvert</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">\bracevert</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">\bracevert</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">|</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">|</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">|</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">|</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">|</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">|</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">∥</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">∥</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">∥</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">∥</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">/</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">/</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">\</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">\</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">⎱</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">⎰</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">\lgroup</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">\rgroup</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">⌞</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">⌟</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" symmetric="true" lspace="thinmathspace">⌜</mo> <mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> </mfrac> <mo form="postfix" fence="true" stretchy="true" symmetric="true" rspace="thinmathspace">⌝</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mi>A</mi> <munderover> <mo stretchy="true" form="infix" lspace="0.277778em" rspace="0.277778em">←</mo> <mspace width="veryverythinmathspace"/> <mrow> <mi>n</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>μ</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>1</mn> </mrow> </munderover> <mi>B</mi> <munderover> <mo stretchy="true" form="infix" lspace="0.277778em" rspace="0.277778em">→</mo> <mi>T</mi> <mrow> <mi>n</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">±</mo> <mi>i</mi> <mo form="infix" lspace="0.222222em" rspace="0.222222em">−</mo> <mn>1</mn> </mrow> </munderover> <mi>C</mi> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>1</mn> <mrow> <msqrt> <mn>2</mn> </msqrt> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>1</mn> <mrow> <msqrt> <mn>3</mn> </msqrt> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>1</mn> <mrow> <msqrt> <mn>4</mn> </msqrt> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>1</mn> <mrow> <msqrt> <mn>5</mn> </msqrt> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mn>1</mn> <mrow> <msqrt> <mn>6</mn> </msqrt> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mi>…</mi> </mrow> </mfrac> </mstyle> </mrow> </mrow> </mfrac> </mstyle> </mrow> </mrow> </mfrac> </mstyle> </mrow> </mrow> </mfrac> </mstyle> </mrow> </mrow> </mfrac> </mstyle> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="true" scriptlevel="0" mathbackground="transparent"> <mrow> <mfrac> <mn>1</mn> <mrow> <msqrt> <mn>2</mn> </msqrt> <mo form="infix" lspace="0.222222em" rspace="0.222222em">+</mo> <mfrac> <mn>1</mn> <mrow> <msqrt> <mn>3</mn> </msqrt> <mo form="infix" lspace="0.000000em" rspace="0.000000em">+</mo> <mfrac> <mn>1</mn> <mrow> <msqrt> <mn>4</mn> </msqrt> <mo form="infix" lspace="0.000000em" rspace="0.000000em">+</mo> <mfrac> <mn>1</mn> <mrow> <msqrt> <mn>5</mn> </msqrt> <mo form="infix" lspace="0.000000em" rspace="0.000000em">+</mo> <mfrac> <mn>1</mn> <mrow> <msqrt> <mn>6</mn> </msqrt> <mo form="infix" lspace="0.000000em" rspace="0.000000em">+</mo> <mi>…</mi> </mrow> </mfrac> </mrow> </mfrac> </mrow> </mfrac> </mrow> </mfrac> </mrow> </mfrac> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em">(</mo> <mfrac linethickness="0px"> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> <mi>M</mi> </mfrac> <mo form="postfix" fence="true" stretchy="true" lspace="0em" rspace="0em">⌋</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em">(</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac linethickness="0px"> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> <mi>M</mi> </mfrac> </mstyle> </mrow> <mo form="postfix" fence="true" stretchy="true" lspace="0em" rspace="0em">⌋</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em">(</mo> <mrow> <mstyle displaystyle="false" scriptlevel="0"> <mfrac linethickness="0px"> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> <mi>M</mi> </mfrac> </mstyle> </mrow> <mo form="postfix" fence="true" stretchy="true" lspace="0em" rspace="0em">⌋</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em">(</mo> <mfrac> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> <mi>M</mi> </mfrac> <mo form="postfix" fence="true" stretchy="true" lspace="0em" rspace="0em">⌋</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em">(</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> <mi>M</mi> </mfrac> </mstyle> </mrow> <mo form="postfix" fence="true" stretchy="true" lspace="0em" rspace="0em">⌋</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em">(</mo> <mrow> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> <mi>M</mi> </mfrac> </mstyle> </mrow> <mo form="postfix" fence="true" stretchy="true" lspace="0em" rspace="0em">⌋</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em">(</mo> <mfrac linethickness="1pt"> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> <mi>M</mi> </mfrac> <mo form="postfix" fence="true" stretchy="true" lspace="0em" rspace="0em">⌋</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em">(</mo> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac linethickness="1pt"> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> <mi>M</mi> </mfrac> </mstyle> </mrow> <mo form="postfix" fence="true" stretchy="true" lspace="0em" rspace="0em">⌋</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mo form="prefix" fence="true" stretchy="true" lspace="0em" rspace="0em">(</mo> <mrow> <mstyle displaystyle="false" scriptlevel="0"> <mfrac linethickness="1pt"> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> <mi>M</mi> </mfrac> </mstyle> </mrow> <mo form="postfix" fence="true" stretchy="true" lspace="0em" rspace="0em">⌋</mo> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mfrac linethickness="0px"> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> <mi>M</mi> </mfrac> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac linethickness="0px"> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> <mi>M</mi> </mfrac> </mstyle> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mstyle displaystyle="false" scriptlevel="0"> <mfrac linethickness="0px"> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> <mi>M</mi> </mfrac> </mstyle> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mfrac> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> <mi>M</mi> </mfrac> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> <mi>M</mi> </mfrac> </mstyle> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mstyle displaystyle="false" scriptlevel="0"> <mfrac> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> <mi>M</mi> </mfrac> </mstyle> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mfrac linethickness="1pt"> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> <mi>M</mi> </mfrac> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mstyle displaystyle="true" scriptlevel="0"> <mfrac linethickness="1pt"> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> <mi>M</mi> </mfrac> </mstyle> </mrow> </mstyle> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mstyle displaystyle="false" scriptlevel="0" mathbackground="transparent"> <mrow> <mstyle displaystyle="false" scriptlevel="0"> <mfrac linethickness="1pt"> <mrow> <mi mathcolor="gray">sin</mi> <mo rspace="0.166667em">⁡</mo> <mi>θ</mi> </mrow> <mi>M</mi> </mfrac> </mstyle> </mrow> </mstyle> </mrow> </mtd> </mtr> </mtable> </math>
Author: Mackichan (S. Swanson)