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-\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}