\section*{Part A}
The function $g$ is defined on $[ 0 ; + \infty [$ by
$$g ( x ) = 1 - \mathrm { e } ^ { - x } .$$
We admit that the function $g$ is differentiable on $[ 0 ; + \infty [$.
\begin{enumerate}
  \item Determine the limit of the function $g$ at $+ \infty$.
  \item Study the variations of the function $g$ on $[ 0 ; + \infty [$ and draw its variation table.
\end{enumerate}