Date: Mon, 16 Jun 2008 14:15:24 +0000
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  pagename=Help%2FTeX2pngPlugin;
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The *~TeX2png* [plugin|Help:WikiPlugin] allows to display mathematical formulae in a Wiki page.

!!! Usage

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

gives

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

!!! 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 | http://www.latex-project.org].

!!! 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 <?plugin TeX2png text="$\textrm{\LaTeX}$" ?> by using :

<verbatim>
<?plugin TeX2png text="$\textrm{\LaTeX}$" ?>
</verbatim>

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 : <?plugin TeX2png text="$\alpha$" ?>, <?plugin TeX2png text="$\beta$" ?>, ... and a formula <?plugin TeX2png text="$\sum_{i=1}^n \frac1{i^2}=\frac{\pi^2}{6}$" ?> to test display in a paragraph.

*Exercise 1* Consider the function <?plugin TeX2png text="$$f(x)=(x^2-4x+3)^{1/2}$$" ?>

#Give the largest real domain for which f(x) is well defined.
#Give a domain on which the function is one-to-one. Using this domain derive a formula for the inverse function <?plugin TeX2png text="$f^{-1}(x)$" ?>.
#Calculate the derivative f'(x).

*Exercise 2* Consider the function :

<?plugin TeX2png text="$$f(x) = \int_0^x e^{-t^2}\,dt, x\in\mathbb R$$" ?>

#Show that for all r > 0 :<?plugin TeX2png text="$$\frac{\pi}{2}\int_0^r t  e^{-t^2}\,dt \leq \int_0^r e^{-x^2}\,dx \int_0^r e^{-y^2}\,dy \leq \frac{\pi}{2} \int_0^{\sqrt{2} r} t e^{-t^2}\,dt$$" ?> *Help* : you can use polar coordinates.
#Hence find the limit of <?plugin TeX2png text="$f(x)$" ?> as x tends <?plugin TeX2png text="to $\infty$" ?>.

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