## This is the LatexRender-ng Project Examples Page

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1.[tex style="background: #ccc; padding: 6px;"]\displaystyle
\Red{\displaystyle e^x=\sum_{n=0}^\infty\frac{x^n}{n!},\ }\Green{\displaystyle e^x=\sum_{n=0}^\infty\frac{x^n}{n!},\ }
\Blue{\displaystyle e^x=\sum_{n=0}^\infty\frac{x^n}{n!}}
[/tex]
The colordvi package is used by default, so you can use named colors:
2.[preamb]
\newcommand{\mycolor}[1]{\Color{0.7 0.8 0.3 0}{#1}}
[/preamb]
$$\displaystyle\mycolor{e=\lim_{x\to +\infty}\left(1+\frac{1}{x}\right)^x}$$
Of course, you can define your own colors!
3.[preamb]\DeclareMathOperator{\tr}{tr}[/preamb]This just adds to the preamble of this page. Nothing should show.
4.The trace of a square matrix $$A$$, denoted $$\tr A$$, is the sum of the elements on its main diagonal.The trace of a square matrix , denoted , is the sum of the elements on its main diagonal.
Note: this uses the macro \tr defined in the preamble.
5.$$\mathbb{R}^n$$
6.[tex fontsize="16"]\mathbb{R}^n[/tex]
7.[tex fontsize="8"]\mathbb{R}^n[/tex]
8.$$x_1+x_2+\cdots+x_n$$
9.$$F_{n+1}=\sum_{k=0}^n{n-k \choose k}$$
10.$$\displaystyle F_{n+1}=\sum_{k=0}^n{n-k \choose k}$$
11.$$n!=n(n-1)(n-2)\cdots 1$$
12.$$\displaystyle (a+b)^n=\sum_{k=0}^n{n\choose k}a^kb^{n-k}$$
13.$$\begin{array}{rcl} (x+y)(x-y)&=&x^2-xy+yx-y^2\\ &=&x^2-y^2;\\ (x+y)^2&=&x^2+2xy+y^2& \end{array}$$
14.[tex style="padding: 4px; border-top: 2px solid #3333ff; border-bottom: 2px solid #3333ff; background: #aaaaee;"]\Red{\det(h_{\lambda_i-i+j})=\pm \det(e_{\mu_i-i+j})}[/tex]
15.$$\begin{array}{rcl} \displaystyle\left(\int_{-\infty}^{+\infty}e^{-x^2}dx\right)^2&=&\displaystyle\int_{-\infty}^{+\infty}\!\!\int_{-\infty}^{+\infty}e^{-x^2-y^2}dx\,dy\\ &=& \displaystyle\int_{0}^{2\pi}\!\!\int_{0}^{+\infty}e^{-r^2}r\,dr\,d\theta\\ &=& \displaystyle\int_{0}^{2\pi}\left(\left.-\frac{e^{-r^2}}{2}\right|_{r=0}^{r=\infty}\right)d\theta \\ &=& \pi \end{array}$$
16.$$\displaystyle \sum_{n=1}^{+\infty}\frac{1}{n^2}=1+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{4^2}+\frac{1}{5^2}+\cdots=\frac{\pi^2}{6}$$
17.Meaningful error messages help out with the authoring.
Unparseable or potentially dangerous latex formula. Error 6: Image was not produced or one of its dimensions is too small.
\begin{align*}{cc}
(x-y)^2 &=&x^2-2xy-y^2;\\
(x+y)^2 &=& x^2+2xy+y^2
\end{align*}

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