\newcommand{\ang}{{\bf {\mathcal A }}}
\newcommand{\bb}{{\bf {\mathcal B }}}
\newcommand{\pp}{{\bf {\mathcal P }}}
\newcommand{\cc}{{\bf C}}
\newcommand{\et}{\mathop{\rm et }}
\newcommand{\etc}{\mathop{\rm etc }}
\newcommand{\ou}{\mathop{\rm ou }}
\newcommand{\Ima}{\mathop{\rm Im }}
\newcommand{\Rea}{\mathop{\rm Re }}
\newcommand{\Ker}{\mathop{\rm Ker }}
\newcommand{\si}{\mathop{\rm si }}
\newcommand{\alors}{\mathop{\rm alors }}
\newcommand{\Arctg}{\mathop{\rm Arg }}
\newcommand{\Arg}{\mathop{\rm Arg }}
\newcommand{\Ch}{\mathop{\rm ch }}
\newcommand{\Sh}{\mathop{\rm sh }}
\newcommand{\Th}{\mathop{\rm th }}
%\newcommand{\ln}{\mathop{\rm ln }}
\newcommand{\sinon}{\mathop{\rm sinon }}
\newcommand{\non}{\mathop{\rm non }}
\newcommand{\rat}{{\bf Q}}
\newcommand{\rr}{{\bf R}}
\newcommand{\rdeu}{{\bf R^2}}
\newcommand{\rrn}{{\bf R^n}}
\newcommand{\nn}{{\bf N}}
\newcommand{\kk}{{\bf K}}
\newcommand{\kx}{{\bf K}[X]}
\newcommand{\rX}{{\bf R}[X]}
\newcommand{\qq}{{\bf Q}}
\newcommand{\zz}{{\bf Z}}
\newcommand{\rar}{\rightarrow}
\newcommand{\imp}{\Longrightarrow}
\newcommand{\limp}{\longleftarrow}
\newcommand{\lrimp}{\longleftrightarrow}
\newcommand{\ssi}{\Longleftrightarrow}
\newcommand{\ove}{\overline}
\documentclass[12pt]{article} \usepackage{vmargin}
\usepackage{amsmath}
\usepackage{amssymb}
\pagestyle{empty} \setmarginsrb{0.5cm}{0.5cm}{1.5cm}{1cm}{1cm}{1cm}{1cm}{1cm}

%\documentstyle[12pt]{article} \pagestyle{empty} \setlength{\textwidth}{13cm}
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\begin{document}

 Maths cc~~~~~~~~~~~~~~~~{\Huge {\bf 
                      ~Exo-type 2 }}  \hfill x/x/x ~Deug MIAS\\ %

		     \vspace{0.6cm}
\noindent
Nom:\\
Documents:\\
Calculette:
		     \vspace{0.6cm}

On consid\`ere les parties de $\rr$ suivantes: 

$$P_0 := \{-x^2 +\pi x +4 | x \in \rr \}
~~~P_1 := \{x^3 -3\pi x +4 | x \in \nn \}
~~~P_2 := \{-x^4 +\pi x +4 | x \in \rat \}$$


$$P_3 := \Ima f ~~~~~~~~~P_4:= f([0,\,+\infty[) ~~~~\text {pour}~~
f:=x \mapsto x +\frac {3\pi}{x+1} $$


$$Q_0 := \{ x \in \rr |e^x >\pi x +4  \}
~~Q_1 := \{ x \in \qq |x-9\le 6\ln x < 2 x -8  \}
~~Q_2 := \{ x \in \nn |x +1 < x^2  \le 6 x +4  \}$$

$$Q_3 :=  f^{-1} (] -3, +\infty[) ~~~~~~~~~ Q_4:= f^{-1} (] -\infty, 2])
 ~~~~\text {pour}~~
f:=x \mapsto \frac {x+3\pi}{x+1}. $$


Remplissez les tableaux suivants, en marquant "?" l\`a o\`u vous pensez qu'il est
normal que vous ne sachiez pas r\'epondre:


\vspace {1cm}


\begin{tabular}{|l|c|c|c|c|c|c|}
\hline
&$P_0$&$P_1$&$P_2$&$P_3$&$P_4$\\ \hline
major\'ee?&~~~~~~~~~~~~~~~~~~~&~~~~~~~~~~~~~~~~~~~&~~~~~~~~~~~~~~~~~~~&~~~~~~~~~~~~~~~~~~~
&~~~~~~~~~~~~~~~~~~~\\ \hline
minor\'ee?&&&&&\\ \hline
born\'ee?&&&&&\\ \hline
sup&&&&&\\ \hline
inf&&&&&\\ \hline
max&&&&&\\ \hline
min&&&&&\\ \hline
\end {tabular}


\vspace {1cm}

\begin{tabular}{|l|c|c|c|c|c|c|}
\hline
&$Q_0$&$Q_1$&$Q_2$&$Q_3$&$Q_4$\\ \hline
major\'ee?&~~~~~~~~~~~~~~~~~~~&~~~~~~~~~~~~~~~~~~~&~~~~~~~~~~~~~~~~~~~&~~~~~~~~~~~~~~~~~~~
&~~~~~~~~~~~~~~~~~~~\\ \hline
minor\'ee?&&&&&\\ \hline
born\'ee?&&&&&\\ \hline
sup&&&&&\\ \hline
inf&&&&&\\ \hline
max=sup?&&&&&\\ \hline
min=inf?&&&&&\\ \hline
\end {tabular}


	\end{document}
