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\input{preamble-standalone.ltx}
\begin{document}
% Ex. No. 61 (Section 14.2 : Courbes de \tkzname{Lorentz})
\begin{tikzpicture}[scale=1]
\tkzInit[xmax=1,ymax=1,xstep=0.1,ystep=0.1]
\tkzGrid(0,0)(1,1)
\tkzAxeXY
\tkzFct[color = red,domain = 0:1]{(exp(\x)-1)/(exp(1)-1)}
\tkzDrawTangentLine[kl=0,kr=0.4,color=red](0)
\tkzDrawTangentLine[kl=0.2,kr=0,color=red](1)
\tkzText[draw,color = red,fill = brown!30](0.4,0.6)%
{$f(x)=\dfrac{\text{e}^x-1}{\text{e}-1}$}
\tkzFct[color = blue,domain = 0:1]{\x*\x*\x}
\tkzDrawTangentLine[kl=0,kr=0.4,color=blue](0)
\tkzDrawTangentLine[kl=0.2,kr=0,color=blue](1)
\tkzText[draw,color = blue,fill = brown!30](0.8,0.1){$g(x)=x^3$}
\tkzFct[color = orange,style = dashed,domain = 0:1]{\x}
\tkzDrawAreafg[between=c and b,color=blue!40,domain = 0:1]
\tkzDrawAreafg[between=c and a,color=red!60,domain = 0:1]
\end{tikzpicture}
\end{document}
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