Math

These math tests are to test MathJax on MyWikis.

$E=m{c}^2$

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

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

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

$\underset{n\to \mathrm{\infty }}{\lim }{x}_n$

$\underset{1}{\overset{3}{\int }}\frac{e^3/x}{x^2}dx$

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

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} }