Date: Tue, 29 Jul 2014 10:42:12 +0000
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The **~TeX2png** [[Help:WikiPlugin|plugin]] allows to display mathematical formulae in a Wiki page.

== Usage ==

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

gives

<<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 [[http://www.latex-project.org | 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 <<TeX2png text="$\textrm{\LaTeX}$">> by using :

{{{
<<TeX2png text="$\textrm{\LaTeX}$">>
}}}

This [[Help:WikiPlugin|plugin]] is not able to produce sophisticated mathematicals texts
with links, cross references... For that, you can use for example
[[http://www.latex2html.org/ | LaTeX2html]].

== Examples ==

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

=== Exercise 1 ===

Consider the function:

<<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 <<TeX2png text="$f^{-1}(x)$">>.
# Calculate the derivative f'(x).

=== Exercise 2 ===

Consider the function:

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

# Show that for all r > 0 :<<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 <<TeX2png text="$f(x)$">> as x tends <<TeX2png text="to $\infty$">>.

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