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\begin{document}

 Maths cc3~~~~~~~~~~~~~~~~{\Huge {\bf 
                      ~Exo-type 3 }}  \hfill x/x/x ~Deug MIAS\\ %

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

On consid\`ere les suites de r\'eels et d'intervalles suivantes: 

$$a_n := \frac {n+1}{n+3}, \,~~~ b_n :=  \left \lfloor\frac {2n+30}{n+1}
\right \rfloor ,~~~
\, c_n := \frac {3n^2 +4}{n^2+1}, \,~~~  d_n := \frac {6n^2 +n}{n^2+1}, \,~~~ 
e_n := \frac {e^{n+2}-1 }{e^{n-2}+1},
$$
$$I_n := ]a_n, b_n[, \,~~~~ J_n := [a_n, c_n], \, ~~~~K_n := ]a_n, e_n[, ~~~~
\, L_n := ]d_n, e_n].$$

~

Renseignez (s'il vous pla\^{\i}t) les tableaux suivants:

~
$$
\begin{array}{|l|c|c|c|c|c|}
\hline
&$a$&$b$&$c$&$d$&$e$\\ \hline
\text {croissante?}&~~~~~~~+~~~~~~~&~~~~~~-~~~~~~~~&~~~~~~~~-~~~~~~
&~~~~~~~-~~~~~~~&~~~~~~~+~~~~~~~
\\ \hline
\text {d\'ecroissante?}		&-&+&+&-&-\\ \hline
\text {scroissante?	}	&+&-&-&-&+\\ \hline
\text {sd\'ecroissante?}	&-&-&+&-&-\\ \hline
\text {stationnaire?}		&-&+&-&-&-\\ \hline
\text {sup}			&1&30&4&876/145&e^4\\ \hline
\text {inf}			&\frac{1}{3}	&2&3&0&\frac{e^6-e^2}{e^2+1}\\ \hline
\text {max}			&\bot		&30&4&876/145&\bot\\ \hline
\text {min	}		&\frac{1}{3}	&2&\bot&0&\frac{e^6-e^2}{e^2+1}\\ \hline
\text {lim}			&1&2&3&6&e^4\\ \hline
\end {array}
$$

\vspace{1cm}

$$
\begin{array}{|l|c|c|c|c|}
\hline
&$I$&$J$&$K$&$L$\\ \hline
\text {croissante?}&-&-&-&-\\ \hline
\text {d\'ecroissante?}		&+&+&-&-\\ \hline
\text {scroissante?}		&-&-&-&-\\ \hline
\text {sd\'ecroissante?}	&+&+&-&-\\ \hline
\text {semboit\'ee?}		&-&+&-&-\\ \hline
\text {sd\'eboit\'ee?}		&-&-&-&-\\ \hline
\text {intersection}		&[1,2[&[1,3]&[1,\frac{e^6-e^2}{e^2+1}[
				&[\frac {876}{145},\frac{e^6-e^2}{e^2+1}[\\ \hline
\text {r\'eunion}		&]\frac {1}{3},30[&[\frac {1}{3},4]
				&[\frac {1}{3},\frac{e^6-e^2}{e^2+1}[
				&[0,\frac{e^6-e^2}{e^2+1}[\\ \hline
\end {array}
$$

	\end{document}
