Math

These math tests are to test MathJax on MyWikis.

$E=mc^{2}$

$f(x)={\sqrt[{3}]{x^{3}}}={\sqrt {x^{2}}}=x=x^{\frac {2}{2}}$

$\theta ={5\pi \over 4}$

$\sin(\theta )=-{{\sqrt {3}} \over 2}$

$\lim _{n\to \infty }x_{n}$

$\int \limits _{1}^{3}{\frac {e^{3}/x}{x^{2}}}\,dx$

${\begin{array}{lll}\int e^{x}\,dx&=e^{x}+C,\\\int \sin x\,dx&=-\cos x+C,\\\int \cos x\,dx&=\sin x+C,\\\int x^{s}\,dx&={\frac {x^{s+1}}{s+1}}+C,\,{\text{ provided }}s\neq 1,\\\int {\frac {1}{x}}\,dx&=\ln |x|+C;\quad {\text{ on intervals}}.\end{array}}$

Failed to parse (unknown function "\newcommand"): {\displaystyle \newcommand{\ra}[1]{\!\!\!\!\!\xrightarrow{\quad#1\quad}\!\!\!\!\!} \newcommand{\da}[1]{\left\downarrow{\scriptstyle#1}\vphantom{\displaystyle\int_0^1}\right.} \newcommand{\la}[1]{\!\!\!\!\!\xleftarrow{\quad#1\quad}\!\!\!\!\!} \newcommand{\ua}[1]{\left\uparrow{\scriptstyle#1}\vphantom{\displaystyle\int_0^1}\right.} % \begin{array}{ccccccccccc} &X & \ra{f} & Y \\ & & _{gf}\searrow & \ \da{g}\\ & & & Z \end{array} \leadsto \begin{array}{ccccccccccc} & {\mathscr F}(X) & \ra{{\mathscr F}(f)} & {\mathscr F}(Y)\\ & & _{{\mathscr F}(gf)}\searrow & \ \ \da{{\mathscr F}(g)}\\ & & & {\mathscr F}(Z) \end{array} \ \text{ and} \begin{array}{cccccccccc} {\mathscr F}(X) & \la{{\mathscr F}(f)} & {\mathscr F}(Y)\\ & _{{\mathscr F}(gf)}\nwarrow & \ \ \ua{{\mathscr F}(g)}\\ & & {\mathscr F}(Z) \end{array} }