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User:Mywikis

2022-02-03T12:18:35Z

Mywikis:

__NUMBEREDHEADINGS__

These '''math tests''' are to test [[mediawikiwiki:Extension:SimpleMathJax|MathJax]] on MyWikis.

<math>E=mc^2</math>

<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>

<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}</math>

<math>
\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}
</math>

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== Good night ==

User:Mywikis

2022-02-02T22:33:33Z

Mywikis: Created page with "These '''math tests''' are to test MathJax on MyWikis. <math>E=mc^2</math> <math> f(x) = \sqrt[3]{x^3} = \sqrt{x^2} = x = x^{\frac{..."

These '''math tests''' are to test [[mediawikiwiki:Extension:SimpleMathJax|MathJax]] on MyWikis.

<math>E=mc^2</math>

<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>

<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}</math>

<math>
\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}
</math>

MediaWiki:Aboutsite

2022-01-21T01:42:47Z