%!TEX TS-program = latex %!TEX encoding = UTF-8 Unicode \documentclass[11pt,a4paper]{article} \usepackage[utf8]{inputenc} %\usepackage[T1]{fontenc} %Enlever si possible le "%" au début de cette ligne \usepackage[french]{babel}\pagestyle{empty} \usepackage{amsfonts,pstricks-add} \begin{document} On considère la fonction $1$-périodique $f \colon \mathbb{R}\to \mathbb{R}$ déterminée par :\\[1mm] \hspace*{\fill} $f(x) = \fontsize{10}{10}\selectfont \left\{\begin{array}{cl} -1&\text{ si } x \in \left]-\frac{1}{2},0\right] \\[0.5mm] 1&\text{ si } x \in \left]0,\frac{1}{2}\right] \end{array}\right.$. \hspace*{\fill}\par\medskip Voici les tracés des graphes des applications $S_{2n-1}(f)$ : \par\vskip5mm\hspace*{\fill} \psset{unit=7cm,algebraic=true}% \begin{pspicture}(-0.55,-1.25)(0.65,1.325) \psaxes[ticks=none,labels=none,arrowscale=1.5]{->}(0,0)(-0.55,-1.25)(0.6,1.3)[$x$,-90][$y$,180] \uput[dl](0,0){$O$} \def\f{0} \multido{\n=1+1}{5}{% \edef\f{\f+4/PI*sin((2*\n-1)*2*PI*x)/(2*\n-1)}% \ifnum\n=1\psplot[linecolor=cyan,plotpoints=100]{-0.5}{0.5}{\f}\fi \ifnum\n=2\psplot[linecolor=orange,plotpoints=200]{-0.5}{0.5}{\f}\fi \ifnum\n=3\psplot[linecolor=green,plotpoints=300]{-0.5}{0.5}{\f}\fi \ifnum\n=4\psplot[linecolor=yellow,plotpoints=400]{-0.5}{0.5}{\f}\fi \ifnum\n=5\psplot[linecolor=magenta,plotpoints=500]{-0.5}{0.5}{\f}\fi } \uput[d](-0.3,0.8){\parbox{2.4cm}{valeurs de $n$ :\\ \color{cyan} 1, \color{orange} 2, \color{green} 3, \color{yellow} 4, \color{magenta} 5}} \end{pspicture}\hspace*{\fill} \end{document}