\documentclass[a4paper]{article} \usepackage{minimum,ifthen,tableau} \usepackage{fancyvrb} \usepackage{fvrb-ex} \fvset{xrightmargin=0cm,frame=none} \newcommand{\coordp}[2] {\begin{pmatrix} #1 \\ #2 \end{pmatrix}} \newpsstyle{hachured}{fillstyle=hlines,hatchwidth=0.2pt,hatchsep=2pt} \usepackage{bbm} \newcommand{\GR}{\mathbbm{R}} \newcommand{\txR}[1][x]{\forall #1 \in \GR \quad} \newcommand{\ssi}[1][,]{si, et seulement si#1 } \begin{document} \begin{verbatim} {\setlength{\TabTitreL}{1cm} \begin{MonTableau}{3}{6}{.75} \small \TabNewCol{0} \rTabPut{Br}{-.15}{.25}{$x$} \rTabPut{Br}{-.15}{.40}{$x$} \rTabPut{Br}{-.15}{.40}{$x^2-12$} \rTabPut{Br}{-.15}{.40}{$f(x)$} \TabNewCol{0} \rTabPut{Bl}{.15}{.25}{$-\infty$} \TabNewCol{.25} \rTabPut{B}{0}{.25}{$-2\sqrt{3}$} \rTabPut[1]{B}{0}{.40}{} \rTabPut[2]{B}{0}{.40}{\TabZ} \rTabPut[2]{B}{0}{.40}{\TabZ} \TabNewCol{.5} \rTabPut{B}{0}{.25}{\TabZ} \rTabPut[2]{B}{0}{.40}{\TabZ} \rTabPut[1]{B}{0}{.40}{} \rTabPut[2]{B}{0}{.40}{\TabZ} \TabNewCol{.75} \rTabPut{B}{0}{.25}{$2\sqrt{3}$} \rTabPut[1]{B}{0}{.40}{} \rTabPut[2]{B}{0}{.40}{\TabZ} \rTabPut[2]{B}{0}{.40}{\TabZ} \TabNewCol{1} \rTabPut{Br}{-.1}{.25}{$+\infty$} \rput(.125,.5){$-$}\rput(.375,.5){$-$}\rput(.625,.5){$+$}\rput(.875,.5){$+$} \rput(.125,1.5){$+$}\rput(.375,1.5){$-$}\rput(.625,1.5){$-$}\rput(.875,1.5){$+$} \rput(.125,2.5){$-$}\rput(.375,2.5){$+$}\rput(.625,2.5){$-$}\rput(.875,2.5){$+$} \end{MonTableau}} \end{verbatim} Ce qui donne: \begin{enumerate} \begin{minipage}{8.2cm} \item $\txR f(x)=x(x-2\sqrt{3})(x+2\sqrt{3})$. \item Un produit de facteur est nul \ssi au moins est de ses facteurs est nul: $$f(x)=0\Leftrightarrow x\in\{-2\sqrt{3};0;2\sqrt{3}\}$$ \item Tableau de signes ci-contre: $$f(x)<0\Leftrightarrow x\in]-\infty;-2\sqrt{3}[\cup]0;2\sqrt{3}[$$ \end{minipage}\hfill \begin{minipage}{7cm} {\setlength{\TabTitreL}{1cm} \begin{MonTableau}{3}{6}{.75} \small \TabNewCol{0} \rTabPut{Br}{-.15}{.25}{$x$} \rTabPut{Br}{-.15}{.40}{$x$} \rTabPut{Br}{-.15}{.40}{$x^2-12$} \rTabPut{Br}{-.15}{.40}{$f(x)$} \TabNewCol{0} \rTabPut{Bl}{.15}{.25}{$-\infty$} \TabNewCol{.25} \rTabPut{B}{0}{.25}{$-2\sqrt{3}$} \rTabPut[1]{B}{0}{.40}{} \rTabPut[2]{B}{0}{.40}{\TabZ} \rTabPut[2]{B}{0}{.40}{\TabZ} \TabNewCol{.5} \rTabPut{B}{0}{.25}{\TabZ} \rTabPut[2]{B}{0}{.40}{\TabZ} \rTabPut[1]{B}{0}{.40}{} \rTabPut[2]{B}{0}{.40}{\TabZ} \TabNewCol{.75} \rTabPut{B}{0}{.25}{$2\sqrt{3}$} \rTabPut[1]{B}{0}{.40}{} \rTabPut[2]{B}{0}{.40}{\TabZ} \rTabPut[2]{B}{0}{.40}{\TabZ} \TabNewCol{1} \rTabPut{Br}{-.1}{.25}{$+\infty$} \rput(.125,.5){$-$}\rput(.375,.5){$-$}\rput(.625,.5){$+$}\rput(.875,.5){$+$} \rput(.125,1.5){$+$}\rput(.375,1.5){$-$}\rput(.625,1.5){$-$}\rput(.875,1.5){$+$} \rput(.125,2.5){$-$}\rput(.375,2.5){$+$}\rput(.625,2.5){$-$}\rput(.875,2.5){$+$} \end{MonTableau}}\vfill \end{minipage} \end{enumerate} \newpage \begin{Example} {\setlength{\TabTitreL}{1cm} \begin{MonTableau}{1}{9}{1.5} \psframe[style=hachured,linestyle=none](.3,1)(.45,0) \TabNewCol{0} \rTabPut{Br}{-.15}{.25}{$x$} \rTabPut{Br}{-.15}{.40}{$f(x)$} \TabNewCol{0} \rTabPut{Bl}{.15}{.25}{$0$} \rTabPut{Bl}{.15}{.60}{$\frac{3}{2}$} \TabNewCol{.30} \rTabPut{B}{0}{.25}{$1$} \rTabPut{Br}{-.15}{.80}{$+\infty$} \psline[style=TabDblBarre](.3,0)(.3,1) \TabNewCol{.45} \rTabPut{B}{0}{.25}{$\frac{3}{2}$} \rTabPut[2]{B}{0}{.10}{\TabZ} \TabNewCol{1} \rTabPut{Br}{-.15}{.25}{$+\infty$} \rTabPut{Br}{-.15}{.40}{$1$} \TabFleche{B1}{C1} \TabFleche{D1}{E1} \end{MonTableau}} \end{Example} \newpage \begin{center} \begin{Example} \begin{MonTableau}{6}{12}{1.2} \TabNewCol{0} \rTabPut{B}{-.75}{.25}{$t$} \rTabPut{B}{-.75}{.20}{\TabTitre{Sgn.}{x'(t)}} \rTabPut{B}{-.75}{.20}{\TabTitre{Var.}{x}} \rTabPut{B}{-.75}{.20}{\TabTitre{Var.}{y}} \rTabPut{B}{-.75}{.20}{\TabTitre{Sgn.}{y'(t)}} \rTabPut{B}{-.75}{.40}{$\vec{T}$} \rTabPut{B}{-.75}{.40}{$m_T$} \TabNewCol{0} \rTabPut{B}{.5}{.25}{$0$} \rTabPut{B}{.5}{.40}{$1,5$} \rTabPut{B}{.5}{.40}{$2$} \rTabPut{B}{.5}{.15}{$0$} \rTabPut{B}{.5}{.40}{$1,5$} \rTabPut{B}{.5}{.40}{$\coordp{1,5}{1,5}$} \rTabPut{B}{.5}{.40}{$1$} % On recopie 4 fois cette dernière colonne et on ajuste \TabNewCol{.25} \rTabPut{B}{0}{.25}{$1$} \rTabPut{B}{0}{.40}{$0$} \rTabPut{B}{0}{.75}{$4$} \rTabPut{B}{0}{.60}{$4$} \rTabPut{B}{0}{.40}{$3$} \rTabPut{B}{0}{.40}{$\coordp{0}{3}$} \rTabPut{B}{0}{.40}{$\infty$} \TabNewCol{.5} \rTabPut{B}{0}{.25}{$2$}\rTabPut{B}{0}{.40}{$-1.5$} \rTabPut{B}{0}{.40}{$2$}\rTabPut{B}{0}{.75}{$6$} \rTabPut{B}{0}{.40}{$0$}\rTabPut{B}{0}{.40}{$\coordp{-1.5}{0}$} \rTabPut{B}{0}{.40}{$0$} \TabNewCol{.75} \rTabPut{B}{0}{.25}{$3$}\rTabPut{B}{0}{.40}{$0$} \rTabPut{B}{0}{.15}{$0$}\rTabPut{B}{0}{.60}{$4$} \rTabPut{B}{0}{.40}{$-2$}\rTabPut{B}{0}{.40}{$\coordp{0}{-2}$} \rTabPut{B}{0}{.40}{$\infty$} \TabNewCol{1} \rTabPut{B}{-.5}{.25}{$4$}\rTabPut{B}{-.5}{.40}{$1$} \rTabPut{B}{-.5}{.40}{$2$}\rTabPut{B}{-.5}{.15}{$0$} \rTabPut{B}{-.5}{.40}{$1,5$}\rTabPut{B}{-.5}{.40}{$\coordp{1}{-1}$} \rTabPut{B}{-.5}{.40}{$-1$} % les signes + et - on fait tout simplement \rput(.145,0.5){$+$}\rput(.145,3.5){$+$} \rput(.375,0.5){$-$}\rput(.375,3.5){$+$} \rput(.625,0.5){$-$}\rput(.625,3.5){$-$} \rput(.850,0.5){$+$}\rput(.850,3.5){$-$} % les flèches \TabFleche{B2}{C2}\TabFleche{C2}{D2}\TabFleche{D2}{E2}\TabFleche{E2}{F2} \TabFleche{B3}{C3}\TabFleche{C3}{D3}\TabFleche{D3}{E3}\TabFleche{E3}{F3} \TabTitreFerme\TabFerme \end{MonTableau} \end{Example} \end{center} \end{document}