Math

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These math tests are to test the extension Math on MyWikis.

$$E=mc^2$$

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

[math] \theta = {5\pi \over 4} [/math]

[math] \sin(\theta) = -{\sqrt{3} \over 2} [/math]

[math] \lim_{n \to \infty}x_n [/math]

[math] \int\limits_{1}^{3}\frac{e^3/x}{x^2}\, dx [/math]

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

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