\documentclass[a4paper,9pt]{article}%{amsart}

% Ewen's additions

\input{/home/ewen/rocketbook/math/.headers/additions.tex}


\usepackage[T1]{fontenc}
\usepackage[utf8]{inputenc}
%\usepackage[metapost]{mfpic}
\usepackage[french]{babel}
\usepackage[pdftex]{graphicx}
\usepackage{ulem}
\usepackage{bookmark}
\usepackage[arrow,curve,matrix]{xy}
\usepackage{amssymb,amsmath,mathrsfs,amsfonts,amsthm}
\usepackage{verbatim,array,enumerate,epsfig}
\usepackage{fancyhdr,lastpage,fancybox,color,shadethm}%,nopageno}
\usepackage{mathrsfs,hyperref}%,variations}
\usepackage[shortlabels]{enumitem}
\usepackage{tikz}
\usetikzlibrary{patterns}
%\usepackage[pdf]{pstricks}
%\usepackage{stmaryrd}%,ifsym}
%\usepackage{pst-all}
%\usepackage{pstricks}
%\usepackage{pstricks-add}
\usepackage{yhmath,marvosym}


% Cours
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%%%FILE NOT FOUND %%\includegraphics[scale=0.2]{Attention.jpg}
\texttt{/!\textbackslash}
\end{minipage}
\begin{minipage}{15.5cm}
#1
\end{minipage}}
\newcommand{\tpp}{..................................................................................................................................................................}

% Fleches
\newcommand{\too}{\rightarrow}
\newcommand{\fl}{\longrightarrow}
\newcommand{\flto}{\longmapsto}
\renewcommand{\iff}{\Leftrightarrow}

% Ensembles de nombres
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\newcommand{\Pb}{\mathbb{P}}
\newcommand{\Z}{\mathbb{Z}}
\newcommand{\N}{\mathbb{N}}
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\newcommand{\Q}{\mathbb{Q}}
\newcommand{\U}{\mathbb{U}}
\newcommand{\PP}{\mathcal{P}}
\newcommand{\Sfk}{\mathfrak{S}}
\newcommand{\II}{\mathbb{I}}

% Constantes de base
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\renewcommand{\geq}{\geqslant}
\newcommand{\e}{\mathrm{e}}
%\renewcommand{\i}{{\bf \mathrm{i}}}
\newcommand{\eps}{\varepsilon}
\newcommand{\fy}{\varepsilon}
\newcommand{\eq}{\Leftrightarrow}

% Ronds dans l'eau
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\newcommand{\bc}{\mathcal{B}}
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\newcommand{\dc}{\mathcal{D}}
\newcommand{\ec}{\mathcal{E}}
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\newcommand{\ic}{\mathcal{I}}
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\newcommand{\mc}{\mathcal{M}}
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\newcommand{\qc}{\mathcal{Q}}
\newcommand{\rc}{\mathcal{R}}
\renewcommand{\sc}{\mathcal{S}}
\newcommand{\uc}{\mathcal{U}}
\newcommand{\vc}{\mathcal{V}}

% Vecteurs
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\newcommand{\mdk}{\mathcal{M}_2(\K)}
\newcommand{\decomp}[2]{\begin{array}{c}|\\#1\\|\end{array}_{#2}}
\newcommand{\Vect}[1]{\mathrm{Vect}\left(#1\right)}

% Geometrie
%\newcommand{\sslash}{\,/\!\!/\,}
\newcommand{\coords}[2]{\vect{#1\\#2}}
\renewcommand{\cooords}[3]{\vect{#1\\#2\\#3}}

% Fonctions usuelles
\newcommand{\cotan}{\mathrm{cotan}}
\newcommand{\ch}{\mathrm{ch}}
\newcommand{\sh}{\mathrm{sh}}
\renewcommand{\th}{\mathrm{th}}
\newcommand{\argch}{\mathrm{argch}}
\newcommand{\argsh}{\mathrm{argsh}}
\newcommand{\argth}{\mathrm{argth}}
\newcommand{\sg}{\mathrm{sg}}
\newcommand{\id}{\mathrm{id}}

% Probabilites
\newcommand{\pet}{\text{\begin{cursive}p\end{cursive}}}
\newcommand{\cul}{\text{\begin{cursive}q\end{cursive}}}
\newcommand{\indic}[1]{\mathds{1}_{#1}}

% Integration
\newcommand{\dx}{~{\rm d}x}
\newcommand{\dy}{~{\rm d}y}
\newcommand{\dt}{~{\rm d}t}
\newcommand{\dr}{~{\rm d}r}
\newcommand{\dtheta}{~{\rm d}\theta}

% Enjolivages
\newcommand{\semisubline}{${}_{{}_{{}_{{}_{{}_{}}}}}$}
\newcommand{\subline}{${}_{{}_{{}_{{}_{{}_{{}_{{}_{}}}}}}}$}
\newcommand{\bigsubline}{${}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{}}}}}}}}}$}
\newcommand{\megasubline}{${}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{}}}}}}}}}}}}$}
\newcommand{\gigasubline}{${}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{}}}}}}}}}}}}}}}}}$}
\newcommand{\supline}{${}^{{}^{{}^{{}^{{}^{{}^{{}^{}}}}}}}$}
%\newcommand{\semisupline}{${}^{{}^{{}^{{}^{{}^{}}}}}$}
\newcommand{\semisupline}{${}^{{}^{{}^{{}^{}}}}$}
\newcommand{\sublined}{{}_{{}_{{}_{{}_{{}_{{}_{{}_{}}}}}}}}
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\newcommand{\gigasublined}{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{{}_{}}}}}}}}}}}}}}}}}}
\newcommand{\dsp}{\displaystyle}
%%%FILE NOT FOUND %% \newcommand{\smiley}{\includegraphics[scale=0.33]{smiley.pdf}}
\newcommand{\smiley}{\texttt{:)}}
%%%FILE NOT FOUND %% \newcommand{\circonspect}{\includegraphics[scale=0.8]{circonspect.jpg}}
\newcommand{\circonspect}{\texttt{[circonspect]}}
%%%FILE NOT FOUND %% \newcommand{\siffle}{\includegraphics[scale=0.8]{siffle.jpg}}
\newcommand{\siffle}{\texttt{[siffle]}}
\newcommand{\cs}{\copyright}
%%%FILE NOT FOUND %% \newcommand{\ds}{\includegraphics[scale=0.15]{Didactique.jpg}}
\newcommand{\ds}{\texttt{[didactique]}}
\newcommand{\ts}{$\bigstar$}
\newcommand{\Chi}{\text{\Large $\chi$}}

% Herve's friendship
\addtolength{\columnsep}{1.5cm}
\setlength{\columnseprule}{0.1pt}
\setlength{\parindent}{0cm}
\addtolength{\hoffset}{-3cm}
\addtolength{\textwidth}{6cm}
\addtolength{\voffset}{-2.25cm}
\addtolength{\textheight}{4.5cm}
%\pagestyle{fancy}

% Romain's friendship
%\newcommand{\tendvers}[3]{#1\underset{#2}{\longrightarrow} #3}
\newcommand{\afaire}{\underbrace{A\times\dots \times  A}_{\mathversion{normal} n \; \text{fois}}}

% Limites
\newcommand{\tenden}[1]{\displaystyle\mathop{\longrightarrow}_{#1}} 
\newcommand{\tendvers}[2]{\displaystyle\mathop{\longrightarrow}_{#1\rightarrow#2}}
\newcommand{\limiteen}[1]{\displaystyle\mathop{\lim}_{#1}}
\newcommand{\limitevers}[2]{\displaystyle\mathop{\lim}_{#1\rightarrow#2}}

% Environnement theoremes
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\newcommand{\afont}{\usefont{T1}{phvrrn}{m}{sc}}
\newcommand{\backfont}{\usefont{U}{Starburst}{xl}{n}}%{\usefont{T1}{bch}{m}{n}}
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\definecolor{thmcolor}{RGB}{7, 42, 200}
\setlength{\shadedtextwidth}{16.8cm}
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{\backfont}% Body font, eg \normalfont, \itshape
{\parindent}% Indent amount (empty = no indent, \parindent = para indent)
{\somefont}% Thm head font, eg \scshape, \bfseries
{\textcolor{thmcolor}{.}}% Punctuation after thm head
{\newline}% Space after thm head (\newline = linebreak)
{\textcolor{thmcolor}{\thmname{#1\subline}#2~\thmnote{:~~ \somefont #3}}}% Thm head spec
\theoremstyle{main}

% Environnement demonstrations
\addto\captionsfrench{\def\proofname{\textsc{D\'emonstration}}}
%%%FILE NOT FOUND %% \renewcommand{\qedsymbol}{\includegraphics[scale=0.3]{smiley.pdf}}%{$\bullet$}
\renewcommand{\qedsymbol}{$\square$}
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\newcommand{\demo}{\begin{_demo}}
\newcommand{\cqfd}{\end{_demo}}
%\newcommand{\Demonstration}{\begin{_demo}}
%\newcommand{\FinDemonstration}{\end{_demo}}
\newcommand{\Demonstration}{D\'emonstration}
\newcommand{\FinDemonstration}{\qed}
% Theoremes
\newcounter{exemple}
\newcounter{remarque}
\newcounter{application}
\newcounter{notation}
\newcommand{\newdef}{\underline}
\newshadetheorem{_th}{Th\'eor\`eme}%[section]
\newshadetheorem{_thdef}[_th]{Th\'eor\`eme-d\'efinition}
\newshadetheorem{_def}{D\'efinition}
\newshadetheorem{_dfin}[_def]{D\'efinition (informelle)}
%\newshadetheorem{_rk}[_th]{Remarque}
\newenvironment{rem}{\medskip \refstepcounter{remarque}\textcolor{black}{\bf Remarque \theremarque}\\[0.15cm]}{}
\newshadetheorem{_lm}{Lemme}
\newtheorem{_ex}{Exemple}
%\newshadetheorem{_conj}[_th]{Conjecture}
\newenvironment{exemple}{\medskip \refstepcounter{exemple}\textcolor{black}{\bf Exemple \theexemple}~}{}
\newenvironment{contrexemple}{\medskip \refstepcounter{exemple}\textcolor{black}{\bf Contre-exemple \theexemple}~}{}
\newenvironment{exemples}{\medskip \refstepcounter{exemple}\textcolor{black}{\bf Exemples \theexemple}~}{}
\newenvironment{appl}{\medskip \refstepcounter{application}\textcolor{black}{\bf Application \theapplication}~}{}
\newenvironment{notation}{\medskip \refstepcounter{notation}\textcolor{black}{\bf Notation \thenotation~~}}{}
\newenvironment{notations}{\medskip \refstepcounter{notation}\textcolor{black}{\bf Notations \thenotation~~}}{}
\newshadetheorem{_prop}{Proposition}
\newshadetheorem{_pd}[_def]{Proposition-D\'efinition}
\newshadetheorem{_cor}{Corollaire}
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\newcommand{\dht}{\end{_thdef}}
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\newcommand{\orp}{\end{_prop}}
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\newcommand{\FinCorollaire}{\end{_cor}}
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\newcommand{\nifd}{\end{_dfin}}
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\newcommand{\FinDefinition}{\end{_def}}
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\newcommand{\FinLemme}{\end{_lm}}
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\newcommand{\nots}{\begin{notations}}
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%\newcommand{\conj}{\begin{_conj}}
%\newcommand{\jonc}{\end{_conj}}
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\newcommand{\qmr}{\end{rem}}

% Exercices
\newcounter{exo}
\newcommand\exo[1][]{\refstepcounter{exo}{\textbf{Exercice~\theexo.~}}}
\newcommand\pb[1][]{\refstepcounter{exo}{\textbf{Probl\`eme~\theexo.~}}}
\newcommand\partie[1][]{\refstepcounter{exo}{\textbf{Partie~\theexo.~}}}
\newcommand\exoc[1][]{\textbf{Exercice~#1.~}}

% Correction
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\newcommand{\cor}[1]{\textcolor{correct}{#1}}
\definecolor{anticorrect}{rgb}{0.4,0.7,0.4}
\newcommand{\anticor}[1]{\textcolor{anticorrect}{\it {#1}}}

% Entete
\fancyhead[L]{{\footnotesize  Lyc\'ee $\blacksquare\blacksquare\blacksquare\blacksquare\blacksquare\blacksquare\blacksquare\ \ \blacksquare\blacksquare\blacksquare\blacksquare\blacksquare\blacksquare$  -  MPSI} }\fancyhead[R]{{\footnotesize  Ann\'ee 2020-2021 -- Cours et compl\'ements}}\renewcommand{\headrulewidth}{0.1pt}
%\fancyfoot[C]{\thepage/\pageref{LastPage}}\renewcommand{\footrulewidth}{0pt}

% Flemmardise
\newcommand{\ie}{\textit{i.\,e.~}}
\newcommand{\cad}{c'est-\`a-dire~}
\newcommand{\Cad}{C'est-\`a-dire~}
\newcommand{\ssi}{si et seulement si~}
\newcommand{\tbv}{tableau de variations~}
\newcommand{\hdr}{hypoth\`ese de r\'ecurrence}
\newcommand{\cste}{\text{constante}}
\newcommand{\recclc}{La propri\'et\'e est vraie au rang $0$, et elle est h\'er\'editaire, elle est donc vraie pour tout entier $n\in\N$.}
\newcommand{\recdclc}{La propri\'et\'e est vraie aux rangs $0$ et $1$, et elle est doublement h\'er\'editaire, elle est donc vraie pour tout entier $n\in\N$.}
\newcommand{\recinit}[1]{La propri\'et\'e est vraie au rang $#1$, et elle est h\'er\'editaire, elle est donc vraie pour tout entier $n\geq#1$.}
\newcommand{\recdouble}[2]{La propri\'et\'e est vraie aux rangs $#1$ et $#2$, et elle est doublement h\'er\'editaire, elle est donc vraie pour tout entier $n\geq#1$.}
\newcommand{\recfclc}[1]{La propri\'et\'e est fortement h\'er\'editaire, elle est donc vraie pour tout entier $n\geq#1$.}
\newcommand{\CN}{condition n\'ecessaire~}
\newcommand{\CS}{condition suffisante~}
\newcommand{\CNS}{condition n\'ecessaire et suffisante~}
\newcommand{\sev}{sous-espace vectoriel~}
\newcommand{\sea}{sous-espace affine~}
\newcommand{\sevs}{sous-espaces vectoriels~}
\newcommand{\seas}{sous-espaces affines~}
\newcommand{\recurrence}[3]{\underline{Initialisation}~:~#1\\\underline{H\'er\'edit\'e}~:~#2\\La propri\'et\'e est donc bien h\'er\'editaire.\\\underline{Conclusion}~:~#3}
\newcommand{\recurre}[4]{\underline{Initialisation}~:~#1\\\underline{H\'er\'edit\'e}~:~#2\\La propri\'et\'e est donc bien h\'er\'editaire.#3\\\underline{Conclusion}~:~#4}
\newcommand{\analysesynthese}[3]{\underline{Analyse}~:~#1\\\underline{Synth\`ese}~:~#2\\\underline{Conclusion}~:~#3}

%demos
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.............................................................................................................................................................................${}^{{}^{{}^{{}^{{}^{}}}}}$\\
.............................................................................................................................................................................${}^{{}^{{}^{{}^{{}^{}}}}}$\\
.............................................................................................................................................................................${}^{{}^{{}^{{}^{{}^{}}}}}$}
\newcommand{\uneligne}{.............................................................................................................................................................................${}^{{}^{{}^{{}^{{}^{}}}}}$}
\newcommand{\unepetiteligne}{.....................................................................................................................................................${}^{{}^{{}^{{}^{{}^{}}}}}$}
\newcommand{\unezolieligne}{...............................................................................................................................................${}^{{}^{{}^{{}^{{}^{}}}}}$}
\newcommand{\unemicroligne}%{\newline}
{................................................................................................${}^{{}^{{}^{{}^{{}^{}}}}}$}
\newcommand{\enumeration}[1]{\begin{enumerate}#1\end{enumerate}}



%\pagestyle{empty}
\pagestyle{fancy}
\date{}
\begin{document}

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