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Cours} +\date{août 2020} + +\DeclareExerciseCollection{banque} +\xsimsetup{ + step=4, +} + +\begin{document} + +\input{exercises.tex} +\printcollection{banque} +\vfill +\printcollection{banque} +\vfill +\printcollection{banque} + +\end{document} diff --git a/TST_sti2d/01_Derivation/exercises.tex b/TST_sti2d/01_Derivation/exercises.tex index 289d275..f17bbaf 100644 --- a/TST_sti2d/01_Derivation/exercises.tex +++ b/TST_sti2d/01_Derivation/exercises.tex @@ -185,5 +185,35 @@ \end{enumerate} \end{exercise} +\begin{exercise}[subtitle={Dérivation}, step={4}, origin={Création}, topics={Dérivation}, tags={Dérivation, technique}] + Déterminer les dérivées des fonctions suivantes + \begin{multicols}{3} + \begin{enumerate} + \item $f(x) = \cos(x) + \sin(x) + 1$ + \item $g(x) = 2\cos(x) + x$ + \item $h(x) = -3\sin(x) + x^2$ + + \item $x(t) = 4t^2 - 1 + \cos(t)$ + \item $y(t) = \sin(t) + 2t - 10$ + \item $z(t) = \cos(t)(4t + 1)$ + + \item $i(x) = \cos(x)\sin(x)$ + \item $j(x) = \dfrac{2\sin(x)}{3}$ + \item $k(x) = \sin(x)(x^2+2)$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{exercise}[subtitle={Tableau de signes}, step={4}, origin={Création}, topics={Dérivation}, tags={Dérivation, technique}] + Tracer le tableau de signe des fonctions suivantes + \begin{multicols}{2} + \begin{enumerate} + \item $f(t) = \sin(t)$ sur $I = \intFF{-2\pi}{2\pi}$ + \item $g(t) = \sin(t)(2t + 1)$ sur $I = \intFF{-\pi}{\pi}$ + \item $h(t) = \sin(t)\cos(t)$ sur $I = \intFF{-\pi}{\pi}$ + \item $h(t) = \dfrac{(t-1)\sin(t)}{t^2}$ sur $I = \intFF{-\pi}{\pi}$ + \end{enumerate} + \end{multicols} +\end{exercise} \collectexercisesstop{banque} diff --git a/TST_sti2d/01_Derivation/index.rst b/TST_sti2d/01_Derivation/index.rst index 54f2192..fdb8227 100644 --- a/TST_sti2d/01_Derivation/index.rst +++ b/TST_sti2d/01_Derivation/index.rst @@ -68,3 +68,10 @@ Définition des fonctions Cos et Sin et introduction de leur dérivée. :height: 200px :alt: Cours sur les fonctions trigonométriques +Exercices techniques d'étude de signe et de calculs de dérivées + + +.. image:: ./4E_trigo.pdf + :height: 200px + :alt: Exercices avec les fonctions trigonométriques +