This exercise is a multiple choice questionnaire (MCQ). For each question, three statements are proposed, only one of these statements is correct.

\begin{enumerate}
  \item Consider the function $f$ defined on $\mathbb{R}$ by
$$f(x) = \left(x^2 - 2x - 1\right)\mathrm{e}^x$$
A. The derivative function of $f$ is the function defined by $f^{\prime}(x) = (2x-2)\mathrm{e}^x$.\\
B. The function $f$ is decreasing on the interval $]-\infty; 2]$.\\
C. $\lim_{x \rightarrow -\infty} f(x) = 0$.

  \item Consider the function $f$ defined on $\mathbb{R}$ by $f(x) = \frac{3}{5 + \mathrm{e}^x}$.

Its representative curve in a coordinate system has:\\
A. only one horizontal asymptote;\\
B. one horizontal asymptote and one vertical asymptote;\\
C. two horizontal asymptotes.

  \item Below is the curve $\mathcal{C}_{f^{\prime\prime}}$ representing the second derivative function $f^{\prime\prime}$ of a function $f$ defined and twice differentiable on the interval $[-3.5; 6]$.\\
A. The function $f$ is convex on the interval $[-3; 3]$.\\
B. The function $f$ has three inflection points.\\
C. The derivative function $f^{\prime}$ of $f$ is decreasing on the interval $[0; 2]$.

  \item Consider the sequence $(u_n)$ defined for every natural integer $n$ by $u_n = n^2 - 17n + 20$.\\
A. The sequence $(u_n)$ is bounded below.\\
B. The sequence $(u_n)$ is decreasing.\\
C. One of the terms of the sequence $(u_n)$ equals 2021.

  \item Consider the sequence $(u_n)$ defined by $u_0 = 2$ and, for every natural integer $n$, $u_{n+1} = 0.75 u_n + 5$.
Consider the following ``threshold'' function written in Python:
\begin{verbatim}
def seuil() :
    u = 2
    n = 0
    while u < 45 :
        u = 0,75*u + 5
        n = n+1
    return n
\end{verbatim}
This function returns:\\
A. the smallest value of $n$ such that $u_n \geqslant 45$;\\
B. the smallest value of $n$ such that $u_n < 45$;\\
C. the largest value of $n$ such that $u_n \geqslant 45$.
\end{enumerate}