% !TeX TXS-program:compile = txs:///pdflatex

\documentclass[margin=5mm]{standalone}
\usepackage[nonpgfplots]{tkz-grapheur}

\begin{document}

\begin{GraphiqueTikz}[x=4.4cm,y=4.4cm,Xmin=-0.25,Xmax=2.25,Xgrille=1,Xgrilles=1,Ymin=-0.25,Ymax=1.25,Ygrille=1,Ygrilles=1]
	\TracerAxesGrilles[Grille=false,Elargir=2.5mm,Origine]{1,2}{0.5,1}
	\TracerCourbe[Couleur=red,Debut=0.5]{ln(x)}
	\TracerCourbe[Couleur=blue]{x-1}
	\PlacerTexte[Police=\Large,Couleur=red]{(1.91,0.568)}{$\mathcal{C}$}
	\PlacerTexte[Police=\Large,Couleur=blue]{(1.91,0.795)}{$T$}
	%points suite u_n
	\filldraw (2,0) circle[radius=2pt] node[above] {$A_{0}$} ;
	\filldraw ({sqrt(2)},0) circle[radius=2pt] node[above] {$A_{1}$} ;
	\filldraw ({sqrt(sqrt(2))},0) circle[radius=2pt] node[above] {$A_{2}$} ;
\end{GraphiqueTikz}

\end{document}