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\input{preamble-standalone.ltx}
\begin{document}
% Ex. No. 45 (Section 10.8 : Asymptote horizontale et verticale)
\begin{tikzpicture}[scale=1.25]
\tkzInit
\tkzGrid
\tkzAxeXY
\tkzFct[color=red,domain=1.001:1.9]{1+1/(log(x-1)**2)}
\tkzFct[color=red,domain = 2.1:10]{1+1/(log(x-1)**2)}
\tkzHLine[line width=1pt,color=red]{1}
\tkzVLine[line width=1pt,color=blue]{2}
\tkzDefPoint(1,1){A}
\tkzDrawPoint[fill=white,color=brown,size=6](A)
\tkzDefPointByFct[draw,with=b]({1+exp(1)})
\tkzLabelPoint[above right](tkzPointResult){$(1+\text{e}~;~2)$}
\tkzText[draw,color = black,fill = brown!20](6,6)%
{$f(x)=\dfrac{1}{\ln^2 (x-1)}+1$}
\end{tikzpicture}
\end{document}
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