%\renewcommand{\theenumi}{\Roman{enumi}}
%\renewcommand{\labelenumiv}{\textbf{\theenumiv.}}

\documentclass{article}%
\usepackage{amssymb}
\usepackage[french]{babel}
\usepackage{geometry}
\usepackage{multicol}
\usepackage{lastpage}
\usepackage[french]{layout}
\usepackage{points}
\usepackage{boxedminipage}
\usepackage{fancybox}
\usepackage{sectsty}
\usepackage{theorem}
\usepackage{amsfonts}
\usepackage{amsmath}
\usepackage{fancyhdr}
\usepackage{afterpage}
\usepackage{array}
\usepackage{graphicx}%
\setcounter{MaxMatrixCols}{30}
%TCIDATA{OutputFilter=latex2.dll}
%TCIDATA{Version=5.00.0.2552}
%TCIDATA{CSTFile=40 LaTeX article.cst}
%TCIDATA{Created=Wednesday, October 15, 2003 19:23:16}
%TCIDATA{LastRevised=Thursday, September 02, 2004 21:01:32}
%TCIDATA{<META NAME="GraphicsSave" CONTENT="32">}
%TCIDATA{<META NAME="SaveForMode" CONTENT="1">}
%TCIDATA{<META NAME="DocumentShell" CONTENT="Articles\SW\DevoirJFil">}
\geometry{
a4paper,
marginpar=2cm,
lmargin=0cm,
rmargin=2cm,
marginparsep=0pt,
includemp=true,
reversemp=true,
headsep=-0.2in
}
\setlength{\theorempostskipamount}{3\baselineskip}
\theoremheaderfont{\large\bfseries}
{  \theorembodyfont{\large\upshape\mdseries}
\theoremstyle{break}
\newtheorem{theorem}{Th�or�me}
}
\newcounter{Cack}[section]
{   \theorembodyfont{\large\upshape}
\theoremstyle{break}
\newtheorem  {acknowledgement}[Cack]{A savoir}
}
\newcounter{Calg}[section]
{  \theorembodyfont{\upshape}
\theoremstyle{break}
\newtheorem{algorithm}[Calg]{M�thode}
}
\newcounter{Caxi}[section]
{   \theorembodyfont{\itshape}
\newtheorem{axiom}[Caxi]{Axiome}
}
\newcounter{Ccas}[section]
{   \theorembodyfont{\upshape}
\newtheorem{case}[Ccas]{Cas}
}
\newcounter{Ccorr}[section]
\renewcommand{\theCcorr}{\Roman{Ccorr}}
{   \theorembodyfont{\upshape}
\theoremstyle{break}
\newtheorem{claim}[Ccorr]{Correction de l'exercice}
}
\newcounter{Cconc}[theorem]
{   \theorembodyfont{\large\mdseries}
\newtheorem{conclusion}[Cconc]{Conclusion}
}
\newcounter{Ccond}[theorem]
{  \theorembodyfont{\large\mdseries}
\newtheorem{condition}[Ccond]{Hypoth�se}
}
\newcounter{Cconj}[section]
{   \theorembodyfont{\upshape}
\newtheorem{conjecture}[Cconj]{Conjecture}
}
\newcounter{Ccor}[section]
{   \theorembodyfont{\upshape}
\newtheorem{corollary}[Ccor]{Corollaire}
}
\newcounter{Ccrit}[section]
{   \theorembodyfont{\upshape}
\newtheorem{criterion}[Ccrit]{Crit�re}
}
\newcounter{Cdef}[section]
\newcounter{Cnot}[section]
{   \theorembodyfont{\large\upshape}
\theoremstyle{break}
\newtheorem{definition}[Cdef]{D�finition}
\newtheorem{notation}[Cnot]{Notation}
}
\newcounter{Cexa}[section]
{   \theorembodyfont{\slshape}
\newtheorem{example}[Cexa]{Exemple}
}
\newcounter{Cexe}[section]
\renewcommand{\theCexe}{\Roman{Cexe}}
{   \theorembodyfont{\upshape}
\theoremstyle{break}
\newtheorem{exercise}[Cexe]{Exercice}
}
\newcounter{Clem}[section]
{   \theorembodyfont{\upshape}
\newtheorem{lemma}[Clem]{Lemme}
}
\newcounter{Cprob}[section]
\renewcommand{\theCprob}
{\Roman{Cprob}.}
{   \theorembodyfont{\upshape}
\theoremstyle{break}
\newtheorem{problem}[Cprob]{Probl�me}
}
{   \theorembodyfont{\large\mdseries}
\newcounter{Cprop}[section]
\theoremstyle{break}
\newtheorem{proposition}[Cprop]{Propri�t�}
}
\newcounter{Crem}[section]
{   \theorembodyfont{\itshape}
\newtheorem{remark}[Crem]{Remarque}
}
\newcounter{Csol}[section]
{   \theorembodyfont{\upshape}
\theoremstyle{break}
\newtheorem{solution}[Csol]{Solution}
}
\newcounter{Csum}[section]
{   \theorembodyfont{\upshape}
\newtheorem{summary}[Csum]{En r�sum�}
}
\newenvironment{proof}[1]
[D�monstration]
{\noindent\textbf{#1:} }
{\ \fbox{cqfd.}
}
\renewcommand{\theenumi}{\arabic{enumi}}
\renewcommand{\theenumii}{\alph{enumii}}
\renewcommand{\theenumiii}{\roman{enumiii}}
\renewcommand{\labelenumi}{\textbf{\theenumi)}}
\renewcommand{\labelenumii}{\textbf{\theenumii)}}
\renewcommand{\labelenumiii}{\textbf{\theenumiii.}}
\newcommand{\LeTitre}{}
\newcommand{\Titre}[1]{\title{#1} \renewcommand
{\LeTitre}{#1}}
\newcommand{\LaClasse}{}
\newcommand
{\Classe}[1]{\renewcommand{\LaClasse} {#1}}
\newcommand{\LaDate}{}
\newcommand
{\Date}[1]{\author{#1}\renewcommand{\LaDate} {#1}}
\newcommand{\Duree}[1]{\date{#1}}
\newcommand{\Letablissement}{}
\newcommand{\Etablissement}[1]{\renewcommand{\Letablissement} {#1}}
\newcommand{\Ladiscipline}{}
\newcommand{\Discipline}[1]{\renewcommand{\Ladiscipline} {#1}}
\renewcommand{\thesection}
{\Alph{section}}
\renewcommand{\thesubsection}
{\thesection\arabic{subsection}}
\renewcommand{\thesubsubsection}
{\thesubsection.\arabic{subsubsection}}
\begin{document}

%%%%%%%%%%b{gedeonInfo}%%%%%%%%%
%%--Document N� 13165932748914--
%%--Ordre et comparaison--
%%%%%%%%%%e{gedeonInfo}%%%%%%%%%
%

%TCIMACRO{\TeXButton{styleDV}{\Etablissement{\large{Nom:\ldots\ldots
%\ldots\ldots\ldots\ldots\ldots}}
%\Discipline{\small{Math�matique}}
%\Titre{Devoir \textit{(surveill�)}  N$^o$2}
%\Classe{\small{Seconde 6}}
%\Date{Le 20 octobre 2003}
%\Duree{Dur�e: 2 heure}
%\maketitle\begin{center}
%\hrulefill\scriptsize{\emph{\textbf
%{ La qualit� de la r�daction et la pr�cision des raisonnements influent sur la notation}%
%}}
%\hrulefill\end{center}
%\fancypagestyle{avecEntete}{
%\lhead{\Letablissement}
%\chead{\small{\LaClasse}}
%\rhead{\small{\Ladiscipline}}
%\lfoot{\scriptsize{Imprim� avec \LaTeXe}}
%\cfoot{}
%\rfoot{\thepage$/$\pageref{LastPage}}
%\renewcommand{\footrulewidth}{0.4pt}
%\renewcommand{\headrulewidth}{0.4pt}
%}
%\fancypagestyle{sansEntete}{
%\renewcommand{\headrulewidth}{0pt}
%\fancyhead{}
%\lfoot{\scriptsize{\LaClasse}}
%\cfoot{\scriptsize{\LeTitre}}
%\rfoot{\thepage$/$\pageref{LastPage}}
%\renewcommand{\footrulewidth}{0.4pt}
%}
%\thispagestyle{avecEntete}
%\pagestyle{sansEntete}}}%
%BeginExpansion
\Etablissement{\large{Nom:\ldots\ldots\ldots\ldots\ldots\ldots\ldots}}
\Discipline{\small{Math�matique}}
\Titre{Devoir \textit{(surveill�)}  N$^o$2}
\Classe{\small{Seconde 6}}
\Date{Le 20 octobre 2003}
\Duree{Dur�e: 2 heure}
\maketitle\begin{center}
\hrulefill\scriptsize{\emph{\textbf
{ La qualit� de la r�daction et la pr�cision des raisonnements influent sur la notation}%
}}
\hrulefill\end{center}
\fancypagestyle{avecEntete}{
\lhead{\Letablissement}
\chead{\small{\LaClasse}}
\rhead{\small{\Ladiscipline}}
\lfoot{\scriptsize{Imprim� avec \LaTeXe}}
\cfoot{}
\rfoot{\thepage$/$\pageref{LastPage}}
\renewcommand{\footrulewidth}{0.4pt}
\renewcommand{\headrulewidth}{0.4pt}
}
\fancypagestyle{sansEntete}{
\renewcommand{\headrulewidth}{0pt}
\fancyhead{}
\lfoot{\scriptsize{\LaClasse}}
\cfoot{\scriptsize{\LeTitre}}
\rfoot{\thepage$/$\pageref{LastPage}}
\renewcommand{\footrulewidth}{0.4pt}
}
\thispagestyle{avecEntete}
\pagestyle{sansEntete}%
%EndExpansion
\label{ForcePass2}

\begin{exercise}
En vous inspirant de l'\'{e}quivalence suivante: $1\leq x\leq3\quad
\Leftrightarrow\quad x\in\lbrack1;3]:$

\begin{enumerate}
\item Traduire en termes d'intervalles:%
\[
-2\leq x\leq3\quad;\quad x\geq-3\quad;\quad x<5\quad;\quad-2\geq x>-5.
\]


\item Traduire en termes d'in\'{e}galit\'{e}s:%
\[
x\in]-\infty;3[\quad;\quad x\in\lbrack-1;1[\quad;\quad x\in]-\infty
;-3[\cup\lbrack4;+\infty\lbrack.
\]

\end{enumerate}
\end{exercise}

\begin{exercise}
$\vspace*{-0.35cm}$

\begin{enumerate}
\item
\begin{enumerate}
\item D\'{e}terminer le signe de $6-2x$ et de $3x-6$ lorsque $x\leq2.$

\item D\'{e}terminer le signe de $6-2x$ et de $3x-6$ lorsque $x\geq3.$

\item En d\'{e}duire le signe de $(6-2x)(3x-6)$ lorsque $x\in]-\infty
;2]\cup\lbrack3;+\infty\lbrack.$
\end{enumerate}

\item En vous inspirant du 1) d\'{e}terminer le signe de $(6-2x)(3x-6)$
lorsque $x\in\lbrack2;3].$

\item Gr\^{a}ce aux r\'{e}ponses trouv\'{e}es au 1) et 2), et \`{a} votre
perspicacit\'{e}, compl\'{e}ter les pointill\'{e}s avec les symboles
$\Longrightarrow$ ou $\Leftrightarrow$ ou $?$ (si aucun des deux symboles
pr\'{e}c\'{e}dents ne convient):%
\[%
\begin{array}
[c]{lll}
&  & \\
(6-2x)(3x-6)\geq0\ldots\ldots\ldots x\in\lbrack2;3] & \quad;\quad &
x\in\lbrack2;3]\ldots\ldots\ldots(6-2x)(3x-6)\geq0\\
&  & \\
(6-2x)(3x-6)>0\ldots\ldots\ldots x\in\lbrack2;3] & \quad;\quad & x\in
\lbrack2;3]\ldots\ldots\ldots(6-2x)(3x-6)>0\\
&  & \\
(6-2x)(3x-6)\geq0\ldots\ldots\ldots x\in\lbrack2;4] & \quad;\quad &
x\in\lbrack2;4]\ldots\ldots\ldots(6-2x)(3x-6)\geq0\\
&  & \\
(6-2x)(3x-6)\leq0\ldots\ldots\ldots x\in]-\infty;2]\cup\lbrack3;+\infty\lbrack
& \quad;\quad & x\in\lbrack3;+\infty\lbrack\ldots\ldots\ldots(6-2x)(3x-6)\leq
0\\
&  & \\
(6-2x)(3x-6)\leq0\ldots\ldots\ldots x\in]-\infty;1]\cup\lbrack3;+\infty\lbrack
& \quad;\quad & x\in]-\infty;0]\ldots\ldots\ldots(6-2x)(3x-6)\leq0
\end{array}
\]

\end{enumerate}
\end{exercise}

\begin{exercise}
$\vspace*{-0.35cm}$

\begin{enumerate}
\item
\begin{enumerate}
\item Soient $a$ et $b$ deux nombres r\'{e}els tels que:%
\[
2<a<3\quad et\quad4<b<5.
\]


Donner un encadrement\ de:%
\[
a+b\quad;\quad ab\quad;\quad a-b\quad;\quad\dfrac{a}{b}.
\]


\item Soient $a$ et $b$ deux nombres r\'{e}els tels que:%
\[
2<a<3\quad et\quad-5<b<-4.
\]


Donner un encadrement \ de $ab.$
\end{enumerate}

\item Soient $x$ et $y$ deux r\'{e}els tels que:%
\[
2<x<3\quad et\quad y<-1.
\]


A-t-on: $-2>xy>-3\quad?$ (expliquer votre r\'{e}ponse).
\end{enumerate}
\end{exercise}

\begin{exercise}
Soit $a$ un nombre r\'{e}el tel que: $0<a<1.$ On pose:%
\[
A=(1-a)\quad;\quad B=(1-a)^{2}\quad;\quad C=\dfrac{1}{1+a}.
\]


\begin{enumerate}
\item Comparer $A$ et $B$ \emph{(on pourra remarquer que }$B=(1-a)\times
A$\emph{)}.

\item Comparer $A$ et $C$ \emph{(on pourra d\'{e}terminer le signe de }%
$A-C$\emph{)}.

\item Ranger $A,$ $B$ et $C$ dans l'ordre croissant.

\item \`{A} l'aide de votre calculatrice, calculer $A,$ $B$ et $C$ pour
$a=4\times10^{-15}.$

Peut-on comparer $A,$ $B$ et $C$ avec la calculatrice pour $a=4\times
10^{-15}\quad?$
\end{enumerate}
\end{exercise}

\begin{exercise}%
%TCIMACRO{\TeXButton{BeginMulticols}{\begin{multicols}{2} }}%
%BeginExpansion
\begin{multicols}{2}
%EndExpansion
Dans la figure ci-contre $ABCD$ est un carr\'{e} inscrit dans un cercle
$\mathcal{C}$. On pose $AB=c.$

\begin{enumerate}
\item D\'{e}montrer que $AC=c\sqrt{2}.$

\item Sachant que:%
\[
3.9<c<4.1\quad et\quad3.14<\pi<3.15
\]


\begin{enumerate}
\item Donner un encadrement de l'aire du carr\'{e}.

\item Donner un encadrement de l'aire du disque\footnote{L'aire d'un disque de
rayon $R$ est $\pi R^{2}$.}.

\item Donner un encadrement de l'aire hachur\'{e}e.
\end{enumerate}
\end{enumerate}

%

\[%
%TCIMACRO{\FRAME{itbpF}{109.5pt}{112.5625pt}{0pt}{}{}{Figure}%
%{\special{ language "Scientific Word";  type "GRAPHIC";
%maintain-aspect-ratio TRUE;  display "USEDEF";  valid_file "T";
%width 109.5pt;  height 112.5625pt;  depth 0pt;  original-width 106.875pt;
%original-height 109.9375pt;  cropleft "0";  croptop "1";  cropright "1";
%cropbottom "0";
%tempfilename 'Include/hnqoah06.wmf';tempfile-properties "XPR";}}}%
%BeginExpansion
\raisebox{-0pt}{\includegraphics[
height=112.5625pt,
width=109.5pt
]%
{Include/i3fgukdd.eps}%
}%
%EndExpansion
\]%
%TCIMACRO{\TeXButton{EndMulticols}{\end{multicols}}}%
%BeginExpansion
\end{multicols}%
%EndExpansion

\end{exercise}

\begin{exercise}
Dans chaque ligne du tableau ci-dessous, $M$ est un point de l'axe r\'{e}el
d'abscisse $x.$ Compl\'{e}ter les pointill\'{e}s et les repr\'{e}sentations
graphiques.\vspace*{0.4cm}

$\hspace{-1.2cm}%
\begin{tabular}
[c]{|c|c|c|c|c|}\hline
\textbf{Repr\'{e}sentation} & \textbf{Encadrement} & \textbf{Intervale} &
\textbf{Distance\footnote{$d(x;y)$ est la distance de $x$ \`{a} $y.$}} &
\textbf{Valeur absolue}\\\hline
\hspace{-0.45cm}%
%TCIMACRO{\FRAME{itbpF}{209.8125pt}{23.5625pt}{10.125pt}{}{}{Figure}%
%{\special{ language "Scientific Word";  type "GRAPHIC";
%maintain-aspect-ratio TRUE;  display "PICT";  valid_file "T";
%width 209.8125pt;  height 23.5625pt;  depth 10.125pt;
%original-width 206.625pt;  original-height 21.4375pt;  cropleft "0";
%croptop "1";  cropright "1";  cropbottom "0";
%tempfilename 'Include/hnqoah07.wmf';tempfile-properties "XPR";}}}%
%BeginExpansion
\raisebox{-10.125pt}{\includegraphics[
height=23.5625pt,
width=209.8125pt
]%
{Include/i3fguldf.eps}%
}%
%EndExpansion
$\quad$ & $-3\leq x\leq6$ & $x\in\ldots\ldots\ldots$ & $d(x;\ldots)\leq\ldots$
& $\left\vert \ldots\ldots\ldots\right\vert \leq\ldots$\\\hline
\hspace{-0.45cm}\textbf{%
%TCIMACRO{\FRAME{itbpF}{209.8125pt}{23.5625pt}{10.125pt}{}{}{Figure}%
%{\special{ language "Scientific Word";  type "GRAPHIC";
%maintain-aspect-ratio TRUE;  display "PICT";  valid_file "T";
%width 209.8125pt;  height 23.5625pt;  depth 10.125pt;
%original-width 206.625pt;  original-height 21.4375pt;  cropleft "0";
%croptop "1";  cropright "1";  cropbottom "0";
%tempfilename 'Include/hnqoah08.wmf';tempfile-properties "XPR";}}}%
%BeginExpansion
\raisebox{-10.125pt}{\includegraphics[
height=23.5625pt,
width=209.8125pt
]%
{Include/i3fgumdh.eps}%
}%
%EndExpansion
}$\quad$ & $\ldots\ldots\ldots$ & $\ldots\ldots\ldots$ & $\ldots\ldots\ldots$
& $\ldots\ldots\ldots$\\\hline
\hspace{-0.45cm}%
%TCIMACRO{\FRAME{itbpF}{209.8125pt}{23.5625pt}{10.125pt}{}{}{Figure}%
%{\special{ language "Scientific Word";  type "GRAPHIC";
%maintain-aspect-ratio TRUE;  display "PICT";  valid_file "T";
%width 209.8125pt;  height 23.5625pt;  depth 10.125pt;
%original-width 206.625pt;  original-height 21.4375pt;  cropleft "0";
%croptop "1";  cropright "1";  cropbottom "0";
%tempfilename 'Include/hnqoah09.wmf';tempfile-properties "XPR";}}}%
%BeginExpansion
\raisebox{-10.125pt}{\includegraphics[
height=23.5625pt,
width=209.8125pt
]%
{Include/i3fgumdj.eps}%
}%
%EndExpansion
$\quad$ & $\ldots\ldots\ldots$ & $x\in]-1;5[$ & $\ldots\ldots\ldots$ &
$\ldots\ldots\ldots$\\\hline
\hspace{-0.45cm}%
%TCIMACRO{\FRAME{itbpF}{209.8125pt}{23.5625pt}{10.125pt}{}{}{Figure}%
%{\special{ language "Scientific Word";  type "GRAPHIC";
%maintain-aspect-ratio TRUE;  display "PICT";  valid_file "T";
%width 209.8125pt;  height 23.5625pt;  depth 10.125pt;
%original-width 206.625pt;  original-height 21.4375pt;  cropleft "0";
%croptop "1";  cropright "1";  cropbottom "0";
%tempfilename 'Include/hnqoah0a.wmf';tempfile-properties "XPR";}}}%
%BeginExpansion
\raisebox{-10.125pt}{\includegraphics[
height=23.5625pt,
width=209.8125pt
]%
{Include/i3fgundl.eps}%
}%
%EndExpansion
$\quad$ & $\ldots\ldots\ldots$ & $\ldots\ldots\ldots$ & $d(x;1)\geq3$ &
$\ldots\ldots\ldots$\\\hline
\hspace{-0.45cm}%
%TCIMACRO{\FRAME{itbpF}{209.8125pt}{23.5625pt}{10.125pt}{}{}{Figure}%
%{\special{ language "Scientific Word";  type "GRAPHIC";
%maintain-aspect-ratio TRUE;  display "PICT";  valid_file "T";
%width 209.8125pt;  height 23.5625pt;  depth 10.125pt;
%original-width 206.625pt;  original-height 21.4375pt;  cropleft "0";
%croptop "1";  cropright "1";  cropbottom "0";
%tempfilename 'Include/hnqoah0b.wmf';tempfile-properties "XPR";}}}%
%BeginExpansion
\raisebox{-10.125pt}{\includegraphics[
height=23.5625pt,
width=209.8125pt
]%
{Include/i3fguodn.eps}%
}%
%EndExpansion
$\quad$ & $\ldots\ldots\ldots$ & $\ldots\ldots\ldots$ & $\ldots\ldots\ldots$ &
$\left\vert x+\tfrac{5}{2}\right\vert \leq\tfrac{3}{2}$\\\hline
\end{tabular}
$
\end{exercise}


\end{document}