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\begin{document}


\begin{center}\section*{\textcolor{red}{2\up{nde} : AP 4 (intervalles}}\end{center}

%\tableofcontents

\subsection{\textcolor{blue}{Intervalles finis}}
Compléter le tableau ci-dessous :

\begin{tabular}{|*{3}{c|}}\hline
Intervalles&Inégalité associée&Représentation\\
\hline
[2~;~5]&$2\leqslant x\leqslant 5$&\psset{xunit=1,yunit=1,comma=true,algebraic=true}
\begin{pspicture}(0,-0.7)(10,0.5)
\psaxes[yAxis=false,Ox=-3]{->}(0,-0.2)(10,0.2)\end{pspicture}
\\
\hline
]-1~;~2]&&\begin{pspicture}(0,-0.7)(10,0.5)
\psaxes[yAxis=false,Ox=-3]{->}(0,-0.2)(10,0.2)\end{pspicture}\\
\hline
[-2~;~3[&&\begin{pspicture}(0,-0.7)(10,0.5)
\psaxes[yAxis=false,Ox=-3]{->}(0,-0.2)(10,0.2)\end{pspicture}\\
\hline
]1~;~4[&&\begin{pspicture}(0,-0.7)(10,0.5)
\psaxes[yAxis=false,Ox=-3]{->}(0,-0.2)(10,0.2)\end{pspicture}\\
\hline
\end{tabular}

\subsection{\textcolor{blue}{Intervalles infinis}}
\begin{tabular}{|*{3}{c|}}\hline
Intervalles&Inégalité associée&Représentation\\
\hline
$[2~;~+\infty[$&$2\leqslant x$&\psset{xunit=1,yunit=1,comma=true,algebraic=true}
\begin{pspicture}(0,-0.7)(10,0.5)
\psaxes[yAxis=false,Ox=-3]{->}(0,-0.2)(10,0.2)\end{pspicture}\\
\hline
$]-1~;~+\infty[$&&\psset{xunit=1,yunit=1,comma=true,algebraic=true}
\begin{pspicture}(0,-0.7)(10,0.5)
\psaxes[yAxis=false,Ox=-3]{->}(0,-0.2)(10,0.2)\end{pspicture}\\
\hline
$]-\infty~;~2[$&&\psset{xunit=1,yunit=1,comma=true,algebraic=true}
\begin{pspicture}(0,-0.7)(10,0.5)
\psaxes[yAxis=false,Ox=-3]{->}(0,-0.2)(10,0.2)\end{pspicture}\\
\hline
$]-\infty~;~1[$&&\psset{xunit=1,yunit=1,comma=true,algebraic=true}
\begin{pspicture}(0,-0.7)(10,0.5)
\psaxes[yAxis=false,Ox=-3]{->}(0,-0.2)(10,0.2)\end{pspicture}\\
\hline
\end{tabular}


\bigskip


\begin{multicols}{2}
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\subsection{\textcolor{blue}{Intersection d'intervalles}}
Déterminer $I \cap J$ dans chacun des cas suivants :

\begin{enumerate}[a)]
\item $I=]-2; 3]$ et $J=]0~;~5]$

\item $I=[-3~;~+\infty[$ et $J=[-10~;~1[$

\bigskip
\item
$I=[-1~;~0]$ et $J=]-1~;~4]$

\bigskip

\item
$ I=]-3~;~4[$ et $J=[3~;~5]$

\bigskip

\item
$I=]-\infty~;~2[$ et $J=[0~;~+\infty[$

\bigskip

\item$I=[3~;~+\infty[$ et $J=]-\infty~;~1]$
\end{enumerate}

\subsection{\textcolor{blue}{Réunion d'intervalles}}
Déterminer $I \cup J$ dans chacun des cas suivants :

\begin{enumerate}[a)]
\item$ I=]-2~;~3]$ et $J=]0~;~5]$

\bigskip

\item t$I=[-3~;~+\infty[$ et $J=[-10~;~1[$

\bigskip

\item  $I=]-\infty~;~1[$ et $J=[0~;~4[$

\bigskip

\item $I=]-3~;~4[$ et $J=[3~;~5]$

\bigskip

\item $I=]-\infty~;~2[$ et $J=[0~;~+\infty[$

\bigskip

\item $I=[-3~;~+\infty[$ et $J=]-\infty~;~1[$
\end{enumerate}


\end{multicols}

\label{fin}
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