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%\begin{titlepage}
{\flushleft
\mbox{\bf NOM:} \hfill \mbox{Licence Sciences \& Technologies}
\\
\mbox{\bf PRENOM:} \hfill\mbox{Fondamentaux des mathématiques I}
\\
\mbox{\bf GROUPE:} \hfill \mbox{Parcours Math. Printemps 2018}}

\vspace{1cm}

\centerline{\large \textbf{Test blanc (15 min - 28 février 2018)} }
%\centerline{\large \textbf{ octobre 2017}}


 \noindent \textbf{Attention: } rédiger directement sur la feuille. Documents, calculatrice, téléphone non autorisés.
 
 
 $ $\\
\noindent \textbf{Question de cours - (6 points) }   

\begin{enumerate}
\item Ecrire le développement limité au point $a=0$ et à l'ordre $n$ de la fonction $x\mapsto \sin x$
\item Enoncer le théorème du rang

\end{enumerate}
  

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\noindent \textbf{Exercice - (8 points)} 
Calculer le développement limité au point $a=0$ à l'ordre $n=2$ de la fonction
$$
f(x)=e^{2x+1}
$$
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\noindent \textbf{Exercice - (8 points)} 

Soit $F_1$ le sous-espace vectoriel de $\mathbb R^3$ engendré par les vecteurs $(2,3,-1)$ et $(1,-1,-2)$.
Soit $F_2$ le sous-espace vectoriel de $\mathbb R^3$ engendré par les vecteurs $(3,2,-3)$ et $(5,0,-7)$. Montrer que $F_1$ et $F_2$ sont égaux.


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