Exercise 3 — 5 points\\
Theme: exponential function, algorithms\\
For each of the following statements, indicate whether it is true or false.\\
Each answer must be justified.\\
An unjustified answer receives no points.
\begin{enumerate}
  \item Statement: The function $f$ defined on $\mathbb{R}$ by $f(x) = \mathrm{e}^x - x$ is convex.
  \item Statement: The equation $(2\mathrm{e}^x - 6)(\mathrm{e}^x + 2) = 0$ has $\ln(3)$ as its unique solution in $\mathbb{R}$.
  \item Statement:
$$\lim_{x \to +\infty} \frac{\mathrm{e}^{2x} - 1}{\mathrm{e}^x - x} = 0.$$
  \item Let $f$ be the function defined on $\mathbb{R}$ by $f(x) = (6x + 5)\mathrm{e}^{3x}$ and $F$ the function defined on $\mathbb{R}$ by: $F(x) = (2x + 1)\mathrm{e}^{3x} + 4$.\\
Statement: $F$ is the antiderivative of $f$ on $\mathbb{R}$ that takes the value 5 when $x = 0$.
  \item We consider the function \texttt{mystere} defined below which takes a list $L$ of numbers as a parameter.\\
We recall that \texttt{len(L)} represents the length of list $L$.
\begin{verbatim}
def mystere(L) :
    S = 0
    for i in range(len(L)) :
        S = S + L[i]
    return S / len(L)
\end{verbatim}
Statement: The execution of \texttt{mystere([1, 9, 9, 5, 0, 3, 6, 12, 0, 5])} returns 50.
\end{enumerate}