complex3.tex

\begin{array}{ll}
{2{\sum{ab}}} & \\
x^{\prime 3} & \\
{{{f^{\prime}{(x)}} + {\sin\cos\theta}} = 1} & \\
{{{f{(z)}} = {\sum\limits_{n = 0}^{\infty}{a_{n}z^{n}}}}\text{, }{{\left| z \right| < R}{({R \neq 0})}}} & \\
{\left. \int{}_{C}{\left( {\sum\limits_{n = 0}^{\infty}{a_{n}z^{n}}} \right){\mathbb{d}z}} \right. = {\sum\limits_{n = 0}^{\infty}{a_{n}\left. \int{}_{C}{z^{n}{\mathbb{d}z}} \right.}}} & \\
{{\lim\limits_{n\rightarrow\infty}\left| \left. \int{}_{C}{\left\lbrack {{f{(z)}} - {\sum\limits_{k = 0}^{n}{a_{k}z^{k}}}} \right\rbrack{\mathbb{d}z}} \right. \right|} = 0} & \\
\left. {n \geq {N{(\varepsilon)}}}\Rightarrow{\left| {{f{(z)}} - {\sum\limits_{k = 0}^{n}{a_{k}z^{k}}}} \right| < \varepsilon} \right. & \\
{{10\text{ Bq}} + {10\text{ Ci}}} & \\
{{10\text{ amol}} + {10\text{ Emol}} - {10\text{ fmol}} + {10\text{ Gmol}} - {10\text{ kmol}} + {10\text{ Mmol}}} & \\
{{10\text{ μmol}} + {10\text{ mmol}} - {10\text{ mol}} + {10\text{ nmol}} - {10\text{ Pmol}} + {10\text{ pmol}} - {10\text{ Tmol}}} & \\
{{10\text{ acre}} + {10\text{ hectare}} - {10\text{ ft}^{2}} + {10\text{ in}^{2}} - {10\text{ m}^{2}}} & \\
{{10\text{ A}} + {10\text{ kA}} - {10\text{ μA}} + {10\text{ mA}} - {10\text{ nA}}} & \\
{{10\text{ F}} + {10\text{ μF}} - {10\text{ mF}} + {10\text{ nF}} - {10\text{ pF}}} & \\
{{10\text{ C}} + {1.0\text{ m/s/s}} - {0.1{\text{ m}/\text{s}^{2}}}} & \\
{{10\text{ kS}} + {10\text{ μS}} - {10\text{ mS}} + {10\text{ S}}} & \\
{{10\text{ kV}} + {10\text{ MV}} - {10\text{ μV}} + {10\text{ mV}} - {10\text{ nV}} + {10\text{ pV}} - {10\text{ V}}} & \\
{{10\text{ GΩ}} + {10\text{ kΩ}} - {10\text{ MΩ}} + {10\text{ mΩ}} - {10\text{ Ω}}} & \\
{{10\text{ Btu}} + {10\text{ cal}} - {10\text{ eV}} + {10\text{ erg}} - {10\text{ GeV}} + {10\text{ GJ}}} & \\
{{10\text{ J}} + {10\text{ kcal}} - {10\text{ kJ}} + {10\text{ MeV}} - {10\text{ MJ}} + {10\text{ μJ}} - {10\text{ mJ}} + {10\text{ nJ}}} & \\
{{10\text{ dyn}} + {10\text{ kN}} - {10\text{ MN}} + {10\text{ μN}} - {10\text{ mN}} + {10\text{ N}} - {10\text{ ozf}} + {10\text{ lbf}}} & \\
{{10\text{ EHz}} + {10\text{ GHz}} - {10\text{ Hz}} + {10\text{ kHz}} - {10\text{ MHz}} + {10\text{ PHz}} - {10\text{ THz}}} & \\
{{10\text{ fc}} + {10\text{ lx}} - {10\text{ phot}}} & \\
{{10\text{ Å}} + {10\text{ am}} - {10\text{ cm}} + {10\text{ dm}} - {10\text{ fm}} + {10\text{ ft}} - {10\text{ in}}} & \\
{{10\text{ km}} + {10\text{ m}} - {10\text{ μm}} + {10\text{ mi}} - {10\text{ mm}} + {10\text{ nm}} - {10\text{ pm}}} & \\
{10\text{ sb}} & \\
{10\text{ lm}} & \\
{10\text{ cd}} & \\
{{10\text{ Mx}} + {10\text{ μWb}} - {10\text{ mWb}} + {10\text{ nWb}} - {10\text{ Wb}}} & \\
{{10\text{ G}} + {10\text{ μT}} - {10\text{ mT}} + {10\text{ nT}} - {10\text{ pT}} + {10\text{ T}}} & \\
{{10\text{ H}} + {10\text{ μH}} - {10\text{ mH}}} & \\
{{10\text{ u}} + {10\text{ cg}} - {10\text{ dg}} + {10\text{ g}} - {10\text{ kg}} + {10\text{ μg}} - {10\text{ mg}} + {10\text{ lb}} - {10\text{ slug}}} & \\
{{10\text{ °}} + {10\text{ μrad}} - {10\text{ mrad}} + {10^{\text{′}}} - {10\text{ rad}} + {10^{\text{′′}}}} & \\
{{10\text{ GW}} + {10\text{ hp}} - {10\text{ kW}} + {10\text{ MW}} - {10\text{ μW}} + {10\text{ mW}} - {10\text{ nW}} + {10\text{ W}}} & \\
{{10\text{ atm}} + {10\text{ bar}} - {10\text{ kbar}} + {10\text{ kPa}} - {10\text{ MPa}} + {10\text{ μPa}} - {10\text{ mbar}} + {10\text{ mmHg}} - {10\text{ Pa}} + {10\text{ torr}}} & \\
{10\text{ sr}} & \\
{{10\text{ °C}} + {10\text{ °F}} - {10\text{ K}}} & \\
{{10\text{ as}} + {10\text{ d}} - {10\text{ fs}} + {10\text{ h}} - {10\text{ μs}} + {10\text{ ms}} - {10\text{ min}} + {10\text{ ns}} - {10\text{ ps}} + {10\text{ s}} - {10\text{ y}}} & \\
{{10\text{ ft}^{3}} + {10\text{ in}^{3}} - {10\text{ m}^{3}} + {10\text{ gal}} - {10\text{ l}}} & \\
{{10\text{ ml}} + {10\text{ pint}} - {10\text{ qt}}} & \\
{\frac{1}{x\left( y \right)} = {\left( {{- {\int{e^{{- \frac{1}{2}}y^{2}}{\sin y}{\mathbb{d}y}}}} + C_{1}} \right)e^{\frac{1}{2}y^{2}}}} & \\
{{{\mathbb{D}_{x}y} - y} = {\sin x}} & \\
{\left( \frac{1}{2} \right)\left( \frac{1}{2} \right)\left( \frac{1}{2} \right)} & \\
{\left\lbrack \frac{1}{2} \right\rbrack\left( \frac{1}{2} \right)\left\{ \frac{1}{2} \right\}} & \\
{\left\langle \frac{1}{2} \right\rangle\left\lfloor \frac{1}{2} \right\rfloor\left\lceil \frac{1}{2} \right\rceil} & \\
{\left. \uparrow\frac{1}{2}\uparrow \right.\left. \downarrow\frac{1}{2}\downarrow \right.\left. \updownarrow\frac{1}{2}\updownarrow \right.} & \\
{\frac{1}{2}\frac{1}{2}\frac{1}{2}} & \\
{\frac{1}{2}\frac{1}{2}\frac{1}{2}} & \\
{\frac{1}{2}\frac{1}{2}\frac{1}{2}} & \\
{{- {({a - b})}} = {b - a}} & \\
{{\frac{2}{5} + \frac{3}{7}} = \frac{{2 \cdot 7} + {3 \cdot 5}}{35} = \frac{29}{35}} & \\
{\left| a \right| = \left\{ \begin{array}{lll}
a & \text{if} & {a \geq 0} \\
{- a} & \text{if} & {a < 0} \\
\end{array} \right.} & \\
{a^{n} = \underset{n\text{ factors}}{\underset{\}\ }{a \cdot a \cdot \cdots \cdot a}}} & \\
{\left( \frac{a}{b} \right)^{- n} = \left( \frac{b}{a} \right)^{n}} & \\
{{\sqrt[n]{a} = b}\text{  means }{b^{n} = a}\text{.}} & \\
{\sqrt[4]{\frac{16}{81}} = \frac{\sqrt[4]{16}}{\sqrt[4]{81}} = \frac{2}{3}} & \\
\left\{ {x \mid {{x \neq 0},{x \neq 1}}} \right\} & \\
{{a_{n}x^{n}} + {a_{n - 1}x^{n - 1}} + \cdots + {a_{1}x} + a_{0}} & \\
{{a^{3} - b^{3}} = {\left( {a - b} \right)\left( {a^{2} + {ab} + b^{2}} \right)}} & \\
{({x + y})}^{2} & \\
{H = \left\{ {{\left( \begin{array}{ll}
a & b \\
c & d \\
\end{array} \right) \in G} \mid {{{ad} - {bc}} = 1}} \right\}} & \\
{{{|x|} + {||y||} + {\{ z\}} - {\lbrack{ac}\rbrack} + {(b)}} = {\lbrack{a,b}\rbrack}} & \\
{x = 1} & \\
{x = 1} & \\
{x = 1} & \\
{x = 1} & \\
{\left\lbrack {{- \frac{10}{3}},{- \frac{7}{3}}} \right) \cup \left( {{- \frac{7}{3}},{- \frac{4}{3}}} \right\rbrack} & \\
{{{A\frac{\partial u}{\partial x}} + {B\frac{\partial u}{\partial y}} + {Cu}} = E} & \\
{\sum\limits_{}^{}x} & \\
{\sum\limits_{\begin{array}{l}
{1 < i < 10} \\
{1 < j < 10} \\
\end{array}}^{}2^{i + j}} & \\
\Gamma_{1_{\mspace{1mu}^{\begin{array}{l}
2_{\mspace{1mu}^{\begin{array}{l}
3 \\
4 \\
\end{array}}}^{} \\
5_{\mspace{1mu}^{\begin{array}{l}
6 \\
7 \\
\end{array}}}^{} \\
\end{array}}}^{}}^{1^{\begin{array}{l}
5^{\begin{array}{l}
7 \\
6 \\
\end{array}} \\
2^{\begin{array}{l}
4 \\
3 \\
\end{array}} \\
\end{array}}} & \\
{{y\left( x \right)} = \frac{{xe^{x}} - e^{x} + 2}{e^{x}} = {x - 1 + \frac{2}{e^{x}}}} & \\
\begin{array}{r}
{{{\mathbb{D}_{xx}y} - y} = 0} \\
{{y{(0)}} = 1} \\
{{y^{\prime}\left( 0 \right)} = 0} \\
\end{array} & \\
{{y\left( x \right)} = {{\frac{1}{3}e^{{- \sqrt[3]{({- 1})}}x}} + {\frac{2}{3}e^{\frac{1}{2}\sqrt[3]{({- 1})}x}{\cos{\frac{1}{2}\sqrt{3}\sqrt[3]{\left( {- 1} \right)}x}}}}} & \\
{{y\left( t \right)} = {2{\tan\left( {{2t} - {\frac{1}{4}\pi}} \right)}}} & \\
{{\mathcal{F}\left( {\begin{array}{l}
e^{2\pi ix} \\
{2\pi{{Dirac}\left( {x - {2\pi}} \right)}} \\
\end{array},x,s} \right)} = \left( \begin{array}{l}
{2\pi{{Dirac}\left( {s - {2\pi}} \right)}} \\
{2\pi e^{{- 2}i\pi s}} \\
\end{array} \right)} & \\
\begin{array}{l}
{x = 1} \\
{{x + 3} = 123} \\
\end{array} & \\
\begin{array}{llll}
t & x & y & z \\
0 & 1.0000 & 1.0000 & 1.0000 \\
.1 & 1.1158 & 1.0938 & .8842 \\
.2 & 1.2668 & 1.1695 & .7332 \\
.3 & 1.4582 & 1.2173 & .5418 \\
.4 & 1.6953 & 1.2253 & .3047 \\
.5 & 1.9830 & 1.1791 & .0170 \\
.6 & 2.3256 & 1.0619 & {- .3256} \\
.7 & 2.7265 & .8542 & {- .7265} \\
.8 & 3.1873 & .5344 & {- 1.1873} \\
.9 & 3.7077 & .0777 & {- 1.7077} \\
1.0 & 4.2842 & {- .5424} & {- 2.2842} \\
\end{array} & \\
{{K_{v}{(z)}} = {{BesselK}_{v}\left( z \right)}} & \\
{{{z^{2}\frac{\mathbb{d}^{2}w}{\mathbb{d}z^{2}}} + {z\frac{\mathbb{d}w}{\mathbb{d}z}} - {\left( {z^{2} + v^{2}} \right)w}} = 0} & \\
{{\frac{\partial^{2}{u{({x,y})}}}{\partial x^{2}} - \frac{\partial^{2}{u{({x,y})}}}{\partial y^{2}}} = 0} & \\
{{y\left( {t,x} \right)} = {{F_{1}\left( {{- x} - {at}} \right)} + {F_{2}\left( {x - {at}} \right)}}} & \\
\begin{array}{lll}
1 & 2 & 3 \\
4 & 5 & 6 \\
\end{array} & \\
{{{2x} + 1} = 5} & \\
\begin{array}{l}
{1 = 3} \\
{9 = 7} \\
\end{array} & \\
\begin{array}{l}
{ab} \\
{cd} \\
{ef} \\
\end{array} & \\
\begin{array}{l}
{{x + {2y} - 3} = 5} \\
{{{4x} - y - 5} = 98} \\
\end{array} & \\
\begin{array}{l}
{x = z} \\
{1 = 3} \\
\end{array} & \\
\begin{array}{l}
{{A_{1} = {{N_{0}{({\lambda;\Omega^{\prime}})}} - {\varphi{({\lambda;\Omega^{\prime}})}}}}\text{,}} \\
{{A_{2} = {{\varphi{({\lambda;\Omega^{\prime}})}} - {\varphi{({\lambda;\Omega})}}}}\text{,}} \\
{{A_{3} = {\mathcal{N}{({\lambda;\omega})}}}\text{.}} \\
\end{array} & \\
\begin{array}{l}
{\sin\theta} \\
{\cos\gamma} \\
\end{array} & \\
{x = \left\{ \begin{array}{ll}
x & {\text{if }{x < 0}} \\
{- x} & {\text{if }{x \geq 0}} \\
\end{array} \right.} & \\
\begin{array}{l}
{LMRM} \\
{LMRM} \\
\end{array} & \\
\begin{array}{l}
{MATH} \\
{MATH} \\
\end{array} & \\
\text{⋮} & \\
{{\operatorname{\nabla\times}F} = 0} & \\
{\operatorname{\nabla}F} & \\
{{\operatorname{\nabla\nabla}F} = {{\nabla^{2}F} + 7} = A} & \\
{{\operatorname{\nabla\times}{({{xy},{yz},{zx}})}} = \left\lbrack \begin{array}{l}
{- y} \\
{- z} \\
{- x} \\
\end{array} \right\rbrack} & \\
{{\operatorname{\nabla\times}{({y,z,x})}} = \left( {{- 1},{- 1},{- 1}} \right) \neq 0} & \\
{{x + y + \alpha} = 102} & \\
{{\mathbf{a} + \mathbf{b}} = \mathbf{c}} & \\
{x + 1} & \\
{{x + {f{(\mathbf{x})}} - 1} = 123} & \\
{{\mathit{T}\mathit{h}\mathit{e}\mathit{q}\mathit{u}\mathit{i}\mathit{c}\mathit{k}brownfoxjumps\mathbf{o}\mathbf{v}\mathbf{e}\mathbf{r}the\mathsf{l}\mathsf{a}\mathsf{z}\mathsf{y}\mathtt{d}\mathtt{o}\mathtt{g}}\text{.}{Theend}\text{.}} & \\
\left( {{\frac{\partial f}{\partial x_{1}}\left( {c_{1},c_{2},\ldots,c_{n}} \right)},{\frac{\partial f}{\partial x_{2}}\left( {c_{1},c_{2},\ldots,c_{n}} \right)},\ldots,{\frac{\partial f}{\partial x_{n1}}\left( {c_{1},c_{2},\ldots,c_{n}} \right)}} \right) & \\
{{\nabla\left( {{cuv} + {v^{2}w}} \right)} = \left( {{uv},{cv},{{cu} + {2vw}},v^{2}} \right)} & \\
\begin{array}{l}
{{D_{u}{f\left( {a,b,c} \right)}} = {{\nabla{f\left( {a,b,c} \right)}} \cdot \mathbf{u}}} \\
{= {{{\frac{\partial f}{\partial x}\left( {a,b,c} \right)}u_{1}} + {{\frac{\partial f}{\partial y}\left( {a,b,c} \right)}u_{2}} + {{\frac{\partial f}{\partial z}\left( {a,b,c} \right)}u_{3}}}} \\
\end{array} & \\
{{\theta \in \left\{ {\pi + {2X_{3}\pi} - \left( {\arccos{\frac{1}{7}\sqrt{14}}} \right)} \middle| {X_{3} \in {\mathbb{Z}}} \right\}},{\theta \in \left\{ {{2X_{4}\pi} - \pi + \left( {\arccos{\frac{1}{7}\sqrt{14}}} \right)} \middle| {X_{4} \in {\mathbb{Z}}} \right\}}} & \\
{P = {A\left( {A^{T}A} \right)^{- 1}A^{T}}} & \\
{{\det\left( \begin{array}{lll}
x & y & 1 \\
a & b & 1 \\
a & d & 1 \\
\end{array} \right)} = {{xb} - {xd} + {ad} - {ab}} = 0} & \\
{{{A\left( \theta \right)}{A\left( {- \theta} \right)}} = {\left\lbrack \begin{array}{ll}
{\cos\theta} & {- {\sin\theta}} \\
{\sin\theta} & {\cos\theta} \\
\end{array} \right\rbrack\left\lbrack \begin{array}{ll}
{\cos\theta} & {\sin\theta} \\
{- {\sin\theta}} & {\cos\theta} \\
\end{array} \right\rbrack}} & \\
{{J{(A)}} = \left\lbrack \begin{array}{llll}
{J_{n_{1}}\left( \lambda_{1} \right)} & 0 & \cdots & 0 \\
0 & {J_{n_{2}}\left( \lambda_{2} \right)} & \cdots & 0 \\
\text{⋮} & \text{⋮} & \text{⋱} & \text{⋮} \\
0 & 0 & \cdots & {J_{n_{k}}\left( \lambda_{k} \right)} \\
\end{array} \right\rbrack} & \\
{{\det\left( \begin{array}{lll}
{{- 4} + X} & {- 1} & 0 \\
0 & {{- 4} + X} & 0 \\
0 & 0 & {{- 4} + X} \\
\end{array} \right)} = \left( {X - 4} \right)^{3}} & \\
\left. \left\{ \left( \begin{array}{l}
{{- \frac{1}{2}} - {\frac{1}{6}\sqrt{33}}} \\
1 \\
\end{array} \right) \right\}\leftrightarrow{\frac{5}{2} - {\frac{1}{2}\sqrt{33}}} \right. & \\
{\left. \parallel A\parallel \right. = {\max\limits_{x \neq 0}\frac{\left. \parallel{Ax}\parallel \right.}{\left. \parallel x\parallel \right.}}} & \\
{{\left( \begin{array}{ll}
a_{11} & a_{12} \\
a_{21} & a_{22} \\
\end{array} \right) + \left( \begin{array}{ll}
b_{11} & b_{12} \\
b_{21} & b_{22} \\
\end{array} \right)} = \left( \begin{array}{ll}
{a_{11} + b_{11}} & {a_{12} + b_{12}} \\
{a_{21} + b_{21}} & {a_{22} + b_{22}} \\
\end{array} \right)} & \\
{{f\left( \left\lbrack \begin{array}{ll}
1 & 2 \\
4 & 3 \\
\end{array} \right\rbrack \right)} = {\left\lbrack \begin{array}{ll}
1 & 2 \\
4 & 3 \\
\end{array} \right\rbrack^{2} - {5\left\lbrack \begin{array}{ll}
1 & 2 \\
4 & 3 \\
\end{array} \right\rbrack} - 2} = \left\lbrack \begin{array}{ll}
2 & {- 2} \\
{- 4} & 0 \\
\end{array} \right\rbrack} & \\
{x = {\lim\limits_{x = 1}{\sum\limits_{1}^{2}a}}} & \\
{{\int_{a}^{b}{{f{(x)}}{\mathbb{d}x}}} = {\lim\limits_{{\parallel P\parallel}\rightarrow 0}{\sum\limits_{i = 1}^{n}{{f\left( {\overline{x}}_{i} \right)}{\Delta x_{i}}}}}} & \\
{{\int_{a}^{b}{{f{(x)}}{\mathbb{d}x}}} = {\lim\limits_{n\rightarrow\infty}{\frac{b - a}{n}{\sum\limits_{i = 1}^{n}{f\left( {a + {i\frac{b - a}{n}}} \right)}}}}} & \\
{{\int_{0}^{2}{x^{5}\sqrt{x^{3} + 1}{\mathbb{d}x}}} = {\int_{1}^{3}{\frac{2}{3}u\frac{\sqrt{\left( u^{2} \right)}}{\left( {u^{2} - 1} \right)^{\frac{2}{3}}}\left( {{u^{2}\left( {u^{2} - 1} \right)^{\frac{2}{3}}} - \left( {u^{2} - 1} \right)^{\frac{2}{3}}} \right){\mathbb{d}u}}}} & \\
{\left. \int{{f{({g{(x)}})}}{g^{\prime}{(x)}}{\mathbb{d}x}} \right. = \left. \int{{f{(u)}}{\mathbb{d}u}} \right.} & \\
{x = {2{\sum\limits_{n = 1}^{100}{n{({n - 1})}}}}} & \\
{{\lim\limits_{x\rightarrow 0}{\sin\left( \frac{1}{x} \right)}} = {{- 1}..1}} & \\
{{h{({i,j})}} = {{{({2 - j})}{g{(i)}}} + {{({j - 1})}{f{({g{(i)}})}}}}} & \\
{\bigtriangleup:\left. \left\lbrack {0,1} \right\rbrack\rightarrow\left\lbrack {0,1} \right\rbrack \right.} & \\
{{0 \bigtriangledown x} = x} & \\
{{x \bigtriangleup y} = {h^{- 1}\left( {{h\left( x \right)}{h\left( y \right)}} \right)}} & \\
{{x \bigtriangleup y} = {f^{- 1}\left( {\max\left\{ {{{f\left( x \right)} + {f\left( y \right)} - 1},0} \right\}} \right)}} & \\
{{x \bigtriangledown y} = {\eta\left( {{\eta\left( x \right)} \bigtriangleup {\eta\left( y \right)}} \right)}} & \\
{{x{\bigtriangleup_{0}y}} = \left\{ \begin{array}{lll}
{x \land y} & \text{if} & {x \vee {y = 1}} \\
0 & \text{if} & {x \vee {y < 1}} \\
\end{array} \right.} & \\
{{\lim\limits_{a\rightarrow 1^{+}}{\log_{a}\left\lbrack {1 + \frac{\left( {a^{x} - 1} \right)\left( {a^{y} - 1} \right)}{a - 1}} \right\rbrack}} = {\lim\limits_{a\rightarrow 1^{-}}{\log_{a}\left\lbrack {1 + \frac{\left( {a^{x} - 1} \right)\left( {a^{y} - 1} \right)}{a - 1}} \right\rbrack}} = {xy}} & \\
{{g{(x)}} = {\exp\left( {- \frac{1 - \left( {1 - x} \right)^{a}}{\left( {2^{a} - 1} \right)\left( {1 - x} \right)^{a}}} \right)}} & \\
{{\operatorname{Aut}{(\mathbf{I})}} = \left\{ {f:\left. \left\lbrack {0,1} \right\rbrack\rightarrow\left\lbrack {0,1} \right\rbrack \right.}\;\left| \begin{array}{l}
{f\text{ is\ one-to-one\ and\ onto,\ and}} \\
{{x \leq y}\text{ implies }{{f\left( x \right)} \leq {f\left( y \right)}}} \\
\end{array} \right. \right\}} & \\
{{{x^{2} + y^{2}} = r^{2}},\text{\quad\quad}{{\tan\theta} = \frac{y}{x}}} & \\
{\sqrt{2}\sqrt{1 - t^{2}}} & \\
\left\lbrack {{{({2 + {\sin t}})}10{\cos t}},{{({2 + {\cos t}})}10{\sin t}},{3{\sin{3t}}}} \right\rbrack & \\
{\left\{ {{t = 0},{s = 0}} \right\},\left\{ {{t = \pi},{s = \pi}} \right\}} & \\
\begin{array}{l}
\begin{array}{llllllllll}
1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 \\
2 & 4 & 6 & 8 & 10 & 1 & 3 & 5 & 7 & 9 \\
3 & 6 & 9 & 1 & 4 & 7 & 10 & 2 & 5 & 8 \\
4 & 8 & 1 & 5 & 9 & 2 & 6 & 10 & 3 & 7 \\
5 & 10 & 4 & 9 & 3 & 8 & 2 & 7 & 1 & 6 \\
6 & 1 & 7 & 2 & 8 & 3 & 9 & 4 & 10 & 5 \\
7 & 3 & 10 & 6 & 2 & 9 & 5 & 1 & 8 & 4 \\
8 & 5 & 2 & 10 & 7 & 4 & 1 & 9 & 6 & 3 \\
9 & 7 & 5 & 3 & 1 & 10 & 8 & 6 & 4 & 2 \\
10 & 9 & 8 & 7 & 6 & 5 & 4 & 3 & 2 & 1 \\
\end{array} \\
\end{array} & \\
\begin{array}{l}
{\text{testing }x^{2}\text{ end.}} \\
\end{array} & \\
\begin{array}{l}
\text{x} \\
\end{array} & \\
\begin{array}{l}
x \\
\end{array} & \\
\begin{array}{l}
\text{x} \\
\end{array} & \\
\begin{array}{l}
x \\
\end{array} & \\
{{\frac{\mathbb{d}f}{\mathbb{d}x}{(x_{1})}} = 5} & \\
{{\int{x{\mathbb{d}x}}} = {\iint{xy{\mathbb{d}x}{\mathbb{d}y}}} = {\iiint{xyz{\mathbb{d}x}{\mathbb{d}y}{\mathbb{d}z}}} = {\iiiint{xyzt{\mathbb{d}x}{\mathbb{d}y}{\mathbb{d}z}{\mathbb{d}t}}}} & \\
{\operatorname{mod}a} & \\
{{5\operatorname{mod}3} = 2} & \\
{{{f{(0)}}\operatorname{mod}3} = 1} & \\
{{{{5x} + 4} \equiv 8}\left( {\operatorname{mod}13} \right)} & \\
{a = {{{({5 - 3})}/5}\operatorname{mod}7} = 6} & \\
{{{\left( {{2x^{2}} + x + 2} \right) + \left( {{2x} + 1} \right)}\operatorname{mod}3} = {2x^{2}}} & \\
\begin{array}{lll}
 + & 0 & 1 \\
000 & 000 & 111 \\
1 & 1 & 0 \\
\end{array} & \\
4.\, 974\, 9 & \\
{\frac{\mathbb{d}}{\mathbb{d}x}{F{(x)}}} & \\
\left\lbrack {86.333,146.33,129.33} \right\rbrack & \\
{{{BinomialDist}{({x;{n,p}})}} = {\sum\limits_{k = 0}^{x}{\left( \frac{n}{k} \right)p^{k}q^{n - k}}}} & \\
{{\Pr{({X \leq 54})}} = {{BinomialDist}{({54;{100,.55}})}} = .45846} & \\
{{k = {\max\left\{ {\left| {\frac{\partial f}{\partial y}{({x,y})}} \right|:{{({x,y})} \in D}} \right\}}}\text{.}} & \\
{m = {\lim\limits_{x\overset{}{\rightarrow}a}\frac{{f{(x)}} - {f{(a)}}}{x - a}}} & \\
{\left| A \right| = \left| \begin{array}{llllll}
a_{11} & a_{12} & \cdot & \cdot & \cdot & a_{1n} \\
a_{21} & a_{22} & \cdot & \cdot & \cdot & a_{2n} \\
 \cdot & \cdot & \cdot & \mspace{1mu} & \mspace{1mu} & \cdot \\
 \cdot & \cdot & \mspace{1mu} & \cdot & \mspace{1mu} & \cdot \\
 \cdot & \cdot & \mspace{1mu} & \mspace{1mu} & \cdot & \cdot \\
a_{n1} & a_{n2} & \cdot & \cdot & \cdot & a_{nn} \\
\end{array} \right| = {{a_{11}A_{11}} + {a_{12}A_{12}} + \cdots + {a_{1n}A_{1n}}}} & \\
{{x = 1}{(\text{hl\ text }x\text{ end.})}} & \\
{{x = 1}{(\text{hl\ to\ URI }x\text{ end})}} & \\
{{x = 1}{(\text{sex})}} & \\
{{x = 1}{(\text{jbm})}} & \\
 & \\
{{{f{(x)}}g{\lbrack y\rbrack}h{\{ z\}}} + {{\lfloor a\rfloor}{\lceil b\rceil}{\langle c\rangle}}} & \\
{\left. \frac{123}{\frac{456}{A}} \right|\left. \parallel\frac{A}{\frac{B}{A}} \right.{\left. /\frac{1}{\frac{2}{A}}/ \right.\left( \frac{3}{\frac{4}{A}} \right)}\left. \updownarrow\frac{5}{\frac{6}{A}}\updownarrow \right.\frac{7}{\frac{8}{A}}\left. \Updownarrow\frac{\frac{9}{20}}{\frac{10}{A}}\Updownarrow \right.{\left. \uparrow\frac{11}{\frac{12}{A}}\uparrow \right.\left. \Uparrow\frac{13}{\frac{14}{A}}\Uparrow \right.}\left. \downarrow\frac{15}{\frac{16}{A}}\downarrow \right.\left. \Downarrow\frac{17}{\frac{18}{A}}\Downarrow \right.} & \\
{x\begin{array}{ll}
x & x \\
x & x \\
\end{array}x} & \\
{{\left( {a_{1},a_{2},\ldots,a_{n}} \right) \cdot \left( {b_{1},b_{2},\ldots,b_{n}} \right)} = {{a_{1}b_{1}^{*}} + {a_{2}b_{2}^{*}} + \cdots + {a_{n}b_{n}^{*}}}} & \\
{\left\lfloor \frac{n}{5} \right\rfloor + \left\lfloor \frac{n}{5^{2}} \right\rfloor + \left\lfloor \frac{n}{5^{3}} \right\rfloor + \left\lfloor \frac{n}{5^{4}} \right\rfloor + \cdots} & \\
{x_{1} + \cdots + x_{n}} & \\
\underset{k\text{ times}}{\underset{\}\ }{x + \cdots + x}} & \\
\sqrt[n]{x_{1}x_{2}\cdots x_{n}} & \\
{{n!} = {1 \times 2 \times 3 \times 4 \times \cdots \times n}} & \\
{P:{a = x_{0} < x_{1} < x_{2} < \cdots < x_{n} = b}} & \\
{{f{(x)}} = {\frac{30}{13{\cos x}} + {\frac{10}{3}\sqrt{\left( {100 + \frac{9}{\cos^{2}x} - {\frac{60}{\cos x}{\sin\left( {x + {\frac{29}{90}\pi}} \right)}}} \right)}}}} & \\
{{\left. \int{{\cos{({Ax})}}{\sin{({Bx})}}{\mathbb{d}x}} \right. = {\frac{- {\cos{{({B - A})}x}}}{2{({B - A})}} + \frac{- {\cos{{({B + A})}x}}}{2{({B + A})}} + C}}\text{ .}} & \\
{{235.3 + 813} = 1048.\, 3} & \\
{{\max\limits_{{- 2} \leq x \leq 2}\left( {x^{3} - {6x} + 3} \right)} = 8.0} & \\
{{x{decade}} = {2{century}}} & \\
{\frac{\mathbb{d}^{5}\left( {x^{7} - {3x^{6}}} \right)}{\mathbb{d}x^{5}}\text{\quad\quad}\frac{\mathbb{d}^{n}{\sin x}}{\mathbb{d}x^{n}}\text{\quad\quad}{\frac{\mathbb{d}^{3}}{\mathbb{d}x^{3}}{f{(x)}}}\text{\quad\quad}{\frac{\mathbb{d}^{2}}{\mathbb{d}t^{2}}\left( {{4t^{5}} - {3t}} \right)}} & \\
{{f{(x)}} = {\frac{30}{13{\cos x}} + {\frac{10}{3}\sqrt{\left( {100 + \frac{9}{\cos^{2}x} - {\frac{60}{\cos x}{\sin\left( {x + {\frac{29}{90}\pi}} \right)}}} \right)}}}} & \\
{\left. \int{}_{\mathbf{R}^{3}}{\left( {\frac{\left| u_{1} \right|^{2} + \left| {\nabla u_{0}} \right|^{2}}{2} + \frac{\left| u_{0} \right|^{6}}{6}} \right){\mathbb{d}x}} \right. < \infty} & \\
{{\left( {\operatorname{\nabla\times}\mathbf{F}} \right) \cdot \mathbf{k}} = {z + 1}} & \\
{M\frac{M^{\frac{M}{M}}}{M}} & \\
{{\mathbb{D}_{x}x^{2}}\text{\quad\quad}{\mathbb{D}_{x}\left( x^{2} \right)}\text{\quad\quad}{\mathbb{D}_{xx}\left( x^{2} \right)}\text{\quad\quad}{\mathbb{D}_{x^{2}}\left( x^{2} \right)}\text{\quad\quad}{\mathbb{D}_{xy}\left( {x^{2}y^{3}} \right)}\text{\quad\quad}{\mathbb{D}_{x^{s}y^{t}}\left( {x^{2}y^{3}} \right)}} & \\
{5\mspace{1mu}{24!}\mspace{1mu} x^{6}} & \\
\begin{array}{l}
\begin{array}{ll}
{x + \sqrt[2]{\frac{a^{y - 1}}{12.34}}} & {\sin\theta} \\
\mspace{1mu} & 1 \\
\end{array} \\
\end{array} & \\
\begin{matrix}
0 & 1 \\
1 & 0 \\
\end{matrix} & \\
\begin{pmatrix}
0 & {- i} \\
i & 0 \\
\end{pmatrix} & \\
\begin{bmatrix}
1 & 0 \\
0 & {- 1} \\
\end{bmatrix} & \\
\left| \begin{matrix}
a & b \\
c & d \\
\end{matrix} \right| & \\
\left. \parallel\begin{matrix}
1 & 0 & 1 \\
0 & 11 & \mspace{1mu} \\
\end{matrix}\parallel \right. & \\
\begin{matrix}
1 & 2 & 3 \\
4 & 5 & \mspace{1mu} \\
\end{matrix} & \\
{\text{testing }\begin{array}{l}
{\sin\theta} \\
\end{array}} & \\
{\widehat{a} + \check{b} + \widetilde{c} + \acute{d} + \grave{e} + \breve{f} + \overline{g} + h + \overset{}{i} + \overset{}{j} + \overset{"}{k} + \dddot{l} + \ddddot{m} + \overset{\rightarrow}{n}} & \\
{{f{({g{(x)}})}} = {{\sin^{3}x^{2}} + {{\sin x^{2}}{\sin\left( {\sin x^{2}} \right)}}}} & \\
{\left( {x^{2} + 12} \right) + 1234} & \\
\begin{array}{lll}
{x = 1} & \text{not} & \text{here} \\
x^{2} & \text{merged} & y_{1} \\
\text{jbm} & \text{lowlife} & \text{The\ end.} \\
\end{array} & \\
{{x^{2} + y^{2}} = {z^{2} - 1}} & \\
\begin{array}{l}
{{x^{2} + y^{2}} = {z^{2} - 1}} \\
{{x + y^{3}} = z^{3}} \\
\end{array} & \\
\begin{array}{l}
{{x^{2} + y^{2}} = {z^{2} - 1}} \\
{{x + y^{3}} = z^{3}} \\
\end{array} & \\
\begin{array}{l}
{{x^{2} + y^{2}} = 1} \\
{x = \sqrt{1 - y^{2}}} \\
\end{array} & \\
\begin{array}{l}
{{({a + b})}^{2} = {a^{2} + {2ab} + b^{2}}} \\
{{{({a + b})} \cdot {({a - b})}} = {a^{2} - b^{2}}} \\
\end{array} & \\
\begin{array}{l}
\text{First\ line\ of\ equation} \\
\text{Middle\ line\ of\ equation} \\
\text{Other\ middle\ line\ of\ equation} \\
\text{Last\ line\ of\ equation} \\
\end{array} & \\
\begin{array}{l}
{{L_{1} = R_{1}}\text{\quad\quad}{L_{2} = R_{2}}} \\
{{L_{3} = R_{3}}\text{\quad\quad}{L_{4} = R_{4}}} \\
\end{array} & \\
\begin{array}{l}
{{({a + b})}^{4} = {{({a + b})}^{2}{({a + b})}^{2}}} \\
{= {{({a^{2} + {2ab} + b^{2}})}{({a^{2} + {2ab} + b^{2}})}}} \\
{= {a^{4} + {4a^{3}b} + {6a^{2}b^{2}} + {4ab^{3}} + b^{4}}} \\
\end{array} & \\
{\begin{array}{l}
{{x^{2} + y^{2}} = 1} \\
{x = \sqrt{1 - y^{2}}} \\
\end{array}\text{\quad\quad}\begin{array}{l}
{{({a + b})}^{2} = {a^{2} + {2ab} + b^{2}}} \\
{{{({a + b})} \cdot {({a - b})}} = {a^{2} - b^{2}}} \\
\end{array}} & \\
\begin{array}{ll}
\text{Vertex} & {V{({0,0})}} \\
\text{Focus} & {F{({0,p})}} \\
\text{Directrix} & {y = {- p}} \\
\end{array} & \\
{{\frac{\mathbb{d}}{\mathbb{d}x}\text{  }{({\csc^{- 1}x})}} = {- \frac{1}{\left| x \right|\sqrt{x^{2} - 1}}}} & \\
{{{\tanh^{- 1}x} = {\frac{1}{2}{\ln\left( \frac{1 + x}{1 - x} \right)}}}\text{\quad\quad}{{- 1} < x < 1}} & \\
{{{\angle\alpha} + {\angle ABC} + {\angle 1}} = {\vartriangle abc}} & \\
{y = {e^{- {\int{P{\mathbb{d}x}}}}\left\lbrack {{\int{e^{\int{P{\mathbb{d}x}}}Q{\mathbb{d}x}}} + c} \right\rbrack}} & \\
{x = {1 + y^{3}}} & {x = {1 + y}} \\
{{\$ 1.00} + {25C/} - {3\pounds} + {2.45} - {0.7Y=} - {aECU} + {20FF} + {30L} - {4.56Pts}} & \\
\begin{array}{l}
{{{2x} + y} = 3} \\
{{{3x} - {4y}} = 5} \\
{{a + b} = {c + 12345}} \\
\end{array} & \\
\begin{array}{lllllll}
\text{Unrestricted} & \text{\quad\quad\quad} & \text{Symmetric} & \quad & \text{Antisymmetric} & \text{\quad\quad} & \text{Triangular} \\
\end{array} & \\
{a \neq b \neq x} & \\
{c \nless d \nless y} & \\
{e \ngtr f \ngtr 11} & \\
{g \notin h \notin Z} & \\
{k \nsim l \nsim 3} & \\
{{A B} \subset C} & \\
{A \nsubseteq B \nsubseteq C} & \\
{10 11 \equiv 12} & \\
{x\operatorname{\nleq{}}y\operatorname{\nleq{}}z} & \\
{\overline{\lim}x} & \\
{\underline{\lim}x} & \\
{\lim\limits_{\rightarrow}x} & \\
{\lim\limits_{\leftarrow}x} & \\
\begin{array}{l}
{x = {y + z}} \\
{= {k + m}} \\
\end{array} & \\
{\begin{array}{l}
{\text{College\ Algebra }\text{Second\ Edition}} \\
{\text{James\ Stewart }\text{McMaster\ Universitiy}} \\
{\text{Lothar\ Redlin}\text{ Pennsylvania\ State\ University}} \\
{\text{Saleem\ Watson}\text{ California\ State\ University,\ Long\ Beach}} \\
\text{Copyright\ 1996,\ ISBN\ 0\ 534-33983-2} \\
\text{Brooks/Cole\ Publishing\ Company} \\
\text{An\ International\ Thomson\ Publishing\ Company} \\
\end{array}\;} & \\
\left\{ \frac{\frac{1}{2}}{\frac{1}{2}}\uparrow\sum\limits_{1}^{2} \right\} & \\
\left\langle \frac{\frac{1}{2}}{\frac{1}{2}} \middle| \sum\limits_{1}^{2} \right\rangle & \\
\left\lceil \frac{\frac{1}{2}}{\frac{1}{2}} \middle| \sum\limits_{1}^{2} \right\rceil & \\
\left. \Downarrow\left. \frac{\frac{1}{2}}{\frac{1}{2}}\updownarrow\sum\limits_{1}^{2} \right.\Downarrow \right. & \\
\left\lbrack \frac{\frac{1}{2}}{\frac{1}{2}} \right\rbrack & \\
\left( \frac{\frac{1}{2}}{\frac{1}{2}} \right) & \\
\left\{ \frac{\frac{1}{2}}{\frac{1}{2}} \right\} & \\
\left\langle \frac{\frac{1}{2}}{\frac{1}{2}} \right\rangle & \\
\left\lfloor \frac{\frac{1}{2}}{\frac{1}{2}} \right\rfloor & \\
\left\lceil \frac{\frac{1}{2}}{\frac{1}{2}} \right\rceil & \\
\left. \uparrow\frac{\frac{1}{2}}{\frac{1}{2}}\uparrow \right. & \\
\left. \downarrow\frac{\frac{1}{2}}{\frac{1}{2}}\downarrow \right. & \\
\left. \updownarrow\frac{\frac{1}{2}}{\frac{1}{2}}\updownarrow \right. & \\
\left. \Uparrow\frac{\frac{1}{2}}{\frac{1}{2}}\Uparrow \right. & \\
\left. \Downarrow\frac{\frac{1}{2}}{\frac{1}{2}}\Downarrow \right. & \\
\left. \Updownarrow\frac{\frac{1}{2}}{\frac{1}{2}}\Updownarrow \right. & \\
\frac{\frac{1}{2}}{\frac{1}{2}} & \\
\left. \backslash arrowvert\frac{\frac{1}{2}}{\frac{1}{2}} \right.\backslash arrowvert & \\
\left. \backslash Arrowvert\frac{\frac{1}{2}}{\frac{1}{2}} \right.\backslash Arrowvert & \\
\left. \backslash bracevert\frac{\frac{1}{2}}{\frac{1}{2}} \right.\backslash bracevert & \\
\left| \frac{\frac{1}{2}}{\frac{1}{2}} \right| & \\
\left| \frac{\frac{1}{2}}{\frac{1}{2}} \right| & \\
\left| \frac{\frac{1}{2}}{\frac{1}{2}} \right| & \\
\left. \parallel\frac{\frac{1}{2}}{\frac{1}{2}}\parallel \right. & \\
\left. \parallel\frac{\frac{1}{2}}{\frac{1}{2}}\parallel \right. & \\
\left. /\frac{\frac{1}{2}}{\frac{1}{2}}/ \right. & \\
\left. \backslash\frac{\frac{1}{2}}{\frac{1}{2}}\backslash \right. & \\
\left. \frac{\frac{1}{2}}{\frac{1}{2}} \right. & \\
\left. \backslash lgroup\frac{\frac{1}{2}}{\frac{1}{2}} \right.\backslash rgroup & \\
\left. \frac{\frac{1}{2}}{\frac{1}{2}} \right. & \\
\left. \frac{\frac{1}{2}}{\frac{1}{2}} \right. & \\
{A\underset{\mspace{1mu}}{\overset{n + \mu - 1}{\leftarrow}}B\underset{T}{\overset{n \pm i - 1}{\rightarrow}}C} & \\
\frac{1}{\sqrt{2} + \frac{1}{\sqrt{3} + \frac{1}{\sqrt{4} + \frac{1}{\sqrt{5} + \frac{1}{\sqrt{6} + \ldots}}}}} & \\
\frac{1}{\sqrt{2} + \frac{1}{\sqrt{3} + \frac{1}{\sqrt{4} + \frac{1}{\sqrt{5} + \frac{1}{\sqrt{6} + \ldots}}}}} & \\
\left( \frac{\sin\theta}{M} \right\rfloor & \\
\left( \frac{\sin\theta}{M} \right\rfloor & \\
\left( \frac{\sin\theta}{M} \right\rfloor & \\
\left( \frac{\sin\theta}{M} \right\rfloor & \\
\left( \frac{\sin\theta}{M} \right\rfloor & \\
\left( \frac{\sin\theta}{M} \right\rfloor & \\
\left( \frac{\sin\theta}{M} \right\rfloor & \\
\left( \frac{\sin\theta}{M} \right\rfloor & \\
\left( \frac{\sin\theta}{M} \right\rfloor & \\
\frac{\sin\theta}{M} & \\
\frac{\sin\theta}{M} & \\
\frac{\sin\theta}{M} & \\
\frac{\sin\theta}{M} & \\
\frac{\sin\theta}{M} & \\
\frac{\sin\theta}{M} & \\
\frac{\sin\theta}{M} & \\
\frac{\sin\theta}{M} & \\
\frac{\sin\theta}{M} & \\
\end{array}