#### Synopsis Help:WikiPlugin to display mathematical formulae in a Wiki page.

#### Usage

<?plugin TeX2png text="$$(a+b)^n=\sum_{k=0}^n{n\choose k}a^k b^{n-k}$$" ?>

gives $(a+b)^n=\sum_{k=0}^n{n\choose k}a^k b^{n-k}$

There is only one argument which is the text of the mathematical expression. This text must be enclosed by a dollar $within a paragraph or two dollars$$on a separate line. In the last case, all is centered. To write mathematical formulae, the syntax is the one of LaTeX. #### Caveats This plugin is only to produce readable mathematical formulae. Any other text is not allowed : so if an expression is not enclosed by dollars then it will be displayed by a red text. It is all the same possible to display raw text as $\textrm{\LaTeX}$ by using : <?plugin TeX2png text="$\textrm{\LaTeX}$" ?> This plugin is not able to produce sophisticated mathematicals texts with links, cross references... For that, you can use for example LaTeX2html. #### Examples Some Greeks letters : $\alpha$, $\beta$, ... and a formula $\sum_{i=1}^n \frac1{i^2}=\frac{\pi^2}{6}$ to test display in a paragraph. Exercise 1 Consider the function $f(x)=(x^2-4x+3)^{1/2}$ 1. Give the largest real domain for which f(x) is well defined. 2. Give a domain on which the function is one-to-one. Using this domain derive a formula for the inverse function $f^{-1}(x)$. 3. Calculate the derivative f'(x). Exercise 2 Consider the function : $f(x) = \int_0^x e^{-t^2}\,dt, x\in\mathbb R$ 1. Show that for all r > 0 : $\frac{\pi}{2}\int_0^r t e^{-t^2}\,dt \leq \int_0^r e^{-x^2}\,dx \int_0^r e^{-y^2}\,dy \leq \frac{\pi}{2} \int_0^{\sqrt{2} r} t e^{-t^2}\,dt$ Help : you can use polar coordinates. 2. Hence find the limit of $f(x)$ as x tends to$\infty\$.

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