$$\newcommand{\N}{\mathbb{N}} \newcommand{\Nn}{\mathbb{N}^*} \newcommand{\Z}{\mathbb{Z}} \newcommand{\R}{\mathbb{R}} \newcommand{\Q}{\mathbb{Q}} \newcommand{\C}{\mathbb{C}} \newcommand{\mcmnr}{\mathcal{M}_n(\mtr)} \newcommand{\mcmnk}{\mathcal{M}_n(\mtk)} \newcommand{\mcsn}{\mathcal{S}_n} \newcommand{\mcs}{\mathcal{S}} \newcommand{\mcd}{\mathcal{D}} \newcommand{\mcsns}{\mathcal{S}_n^{++}} \newcommand{\glnk}{GL_n(\mtk)} \newcommand{\mnr}{\mathcal{M}_n(\mtr)} \DeclareMathOperator{\ch}{ch} \DeclareMathOperator{\sh}{sh} \DeclareMathOperator{\th}{th} \DeclareMathOperator{\vect}{vect} \DeclareMathOperator{\card}{card} \DeclareMathOperator{\comat}{comat} \DeclareMathOperator{\imv}{Im} \DeclareMathOperator{\rang}{rg} \DeclareMathOperator{\Fr}{Fr} \DeclareMathOperator{\diam}{diam} \DeclareMathOperator{\supp}{supp} \newcommand{\veps}{\varepsilon} \newcommand{\mcu}{\mathcal{U}} \newcommand{\mcun}{\mcu_n} \newcommand{\dis}{\displaystyle} \newcommand{\croouv}{[\![} \newcommand{\crofer}{]\!]} \newcommand{\rab}{\mathcal{R}(a,b)} \newcommand{\pss}[2]{\langle #1,#2\rangle} \newcommand{\comb}[2]{{{\Large C}}$_{#1}^{\raisebox{1mm}{\scriptsize{$#2$}}}$} \newenvironment{equations}{\equation\aligned}{\endaligned\endequation} \newenvironment{systeme}{% \left\lbrace \begin{array}{l} }{% \end{array} \right. } %%% Sommes \newcommand{\somme}[4]{\ensuremath{\sum_{#1=#2}^{#3}{#4}}} \newcommand{\Somme}[4]{\ensuremath{\displaystyle\sum_{#1=#2}^{#3}{#4}}} %%% LIMITES \newcommand{\tendvers}{\ensuremath{\longrightarrow}\xspace} % limite quand #1 tend vers #2 \newcommand{\li}[2]{\lim \limits_{#1\rightarrow #2 } } % limite quand #1 tend vers #2 أ  gauche ou أ  droite (#3 = < ou >) \newcommand{\limite}[3]{\lim \limits_{#1\to #2 \atop #1 #3 #2}\,} %Limites \newcommand{\Lim}[2][x]{\displaystyle{\lim_{#1 \rightarrow #2}}} %%% SUITES %%% taper \suite un \newcommand{\suite}[2]{\bigl(#1_#2\bigr)_{#2\in \N}} %---- Les intervalles ---- \newcommand{\intf}[2]{\left[ #1 ; #2 \right]} \newcommand{\into}[2]{\left] #1 ; #2 \right[} \newcommand{\intfo}[2]{\left[ #1 ; #2 \right[} \newcommand{\intof}[2]{\left] #1 ; #2 \right]}%---- Les intervalles ---- %%% INTEGRALES %\newcommand{\integrale}[4]{\displaystyle \int_{#1}^{#2}{\!{#3}({#4})\,d{#4}}} \newcommand{\integrale}[4]{\displaystyle \int_{#1}^{#2}{\!{#3}\,\mathrm{d}{#4}}} \newcommand{\intabfx}{\integrale{a}{b}{f(x)}{x}\xspace} \newcommand{\intabx}[1]{\integrer{a}{b}{#1}{x}\xspace} \newcommand{\applica}[3]{$#1 : #2 \longrightarrow #3$} \newcommand{\fonc}[1]{Soit $f$ la fonction dأ©finie sur $#1$ par } \newcommand{\fonction}[5] {\begin{array}[t]{cccl}#1:&#2&\rightarrow&#3\\&#4&\mapsto&#5\end{array}} \newcommand \syst[4]{ \begin{cases} #1=#2&\\ #3=#4& \end{cases}} \newcommand \syste[4]{ \begin{cases} #1& #2\\ #3 & #4 \end{cases}}$$

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