TeX2pngPlugin user: readonly Collection:  StFlorian Page:  TeX2pngPlugin Last edit:  25/11/09 17:26  by  admin Ver:  1 Hits:  763

# Te X2 png Plugin

### Synopsis

WikiPlugin to display mathematical formulae in a Wiki page.

### Usage

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

gives

$(a+b)^n=sum_{k=0}^n{nchoose k}a^k b^{n-k}$

### Arguments

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 :

$f(x) = int_0^x e^{-t^2},dt, xinmathbb R$
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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