From 682894dfe5e86cb01f219afcd618a0b35ceb98f4 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Fri, 8 May 2020 12:05:41 +0200 Subject: [PATCH] Feat: presque fin du chapitre sur Log pour TESL --- .../Etude_fonction/3B_primitive.pdf | Bin 0 -> 41041 bytes .../Etude_fonction/3B_primitive.tex | 29 +++++++++++++ .../Etude_fonction/3E_primitive.pdf | Bin 0 -> 61357 bytes .../Etude_fonction/3E_primitive.tex | 23 ++++++++++ TES/Logarithme/Etude_fonction/banque.tex | 41 ++++++++++++++++++ TES/Logarithme/Etude_fonction/index.rst | 14 +++++- TES/semaines.rst | 14 +++++- 7 files changed, 119 insertions(+), 2 deletions(-) create mode 100644 TES/Logarithme/Etude_fonction/3B_primitive.pdf create mode 100644 TES/Logarithme/Etude_fonction/3B_primitive.tex create mode 100644 TES/Logarithme/Etude_fonction/3E_primitive.pdf create mode 100644 TES/Logarithme/Etude_fonction/3E_primitive.tex diff --git a/TES/Logarithme/Etude_fonction/3B_primitive.pdf b/TES/Logarithme/Etude_fonction/3B_primitive.pdf new 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des variations} +\tribe{Terminale TESL} +\date{Mai 2020} + +\pagestyle{empty} +\geometry{left=10mm,right=10mm, top=10mm} + +\renewcommand{\baselinestretch}{0.8} + +\DeclareExerciseCollection{banque} +\xsimsetup{ + step=3, +} + +\begin{document} + +\input{banque.tex} +\printcollection{banque} + +\end{document} diff --git a/TES/Logarithme/Etude_fonction/banque.tex b/TES/Logarithme/Etude_fonction/banque.tex index ca838c4..bc19af3 100644 --- a/TES/Logarithme/Etude_fonction/banque.tex +++ b/TES/Logarithme/Etude_fonction/banque.tex @@ -126,4 +126,45 @@ \end{enumerate} \end{exercise} +\begin{exercise}[subtitle={Primitives}, step={3}, topics={Logarithme}] + Calculer les primitives des fonctions suivantes + \begin{multicols}{2} + \begin{enumerate} + \item $f(x) = \dfrac{1}{x} + x$ + \item $g(x) = -\dfrac{4}{x}$ + \item $h(x) = 5x + \dfrac{10}{x}$ + \item $i(t) = 2t + \dfrac{4}{t} - 2\dfrac{1}{t^2}$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{exercise}[subtitle={Coût de fabrication}, step={3}, topics={Logarithme}] + Un usine fabrique entre \np{1000} et \np{7000} objets pas semaines. + + Un étude des moyens de productions a permis de modéliser les coûts de production par la fonction $C$ définie sur $\intFF{1}{7}$ par + \[ + c(x) = 1,5x^2 - 9x + 24 + \dfrac{48}{x} + \] + où $x$ représente la production hebdomadaire en milliers d'objets. + \begin{enumerate} + \item Étude des variations des coûts. + \begin{enumerate} + \item Démontrer que la dérivée de $c$ est + \[ + c'(x) = \frac{3(x-4)(x^2+x+4)}{x^2} + \] + \item Étudier le signe de $c'$ et en déduire les variations de $c$ + \item Pour quelle production les coûts de productions sont-ils minimal? + \end{enumerate} + \item Étude des coûts de productions moyen. + \begin{enumerate} + \item Démontrer qu'une primitive de $c$ est + \[ + C(x) = 0.5x^3 - 4,5x^2 + 24x + 1 + 48\ln(x) + \] + \item Calculer la valeur moyenne de $c$ sur $\intFF{1}{7}$. + \item Interpréter le résultat précédent. + \end{enumerate} + \end{enumerate} +\end{exercise} \collectexercisesstop{banque} diff --git a/TES/Logarithme/Etude_fonction/index.rst b/TES/Logarithme/Etude_fonction/index.rst index f23b1c8..2e59810 100644 --- a/TES/Logarithme/Etude_fonction/index.rst +++ b/TES/Logarithme/Etude_fonction/index.rst @@ -2,7 +2,7 @@ #################################################################### :date: 2020-05-05 -:modified: 2020-05-07 +:modified: 2020-05-08 :authors: Bertrand Benjamin :category: TESL :tags: Logarithme @@ -34,6 +34,18 @@ Cours sur la représentation graphique du logarithme et les formules de dérivat Étape 3: Calculs d'aires ======================== +Cours: + +.. image:: 3B_primitive.pdf + :height: 200px + :alt: Primitive de 1/x + +Exercices + +.. image:: 3E_primitive.pdf + :height: 200px + :alt: Exercices de calculs de primitives avec ln + Étape 4: Annales Bac ==================== diff --git a/TES/semaines.rst b/TES/semaines.rst index c3af337..8f3cdd6 100644 --- a/TES/semaines.rst +++ b/TES/semaines.rst @@ -2,7 +2,7 @@ Programmes semaine par semaine pendant le confinement avec les TLES ################################################################### :date: 2020-04-15 -:modified: 2020-05-07 +:modified: 2020-05-08 :authors: Bertrand Benjamin :category: TESL :tags: Progression @@ -80,6 +80,18 @@ S20 - Logarithme - étude de la fonction (2h15) :height: 200px :alt: Exercices d'étude de fonctions avec le logarithme. +- Cours: Primitive de $\frac{1}{x}$ + +.. image:: ./Logarithme/Etude_fonction/3B_primitive.pdf + :height: 200px + :alt: Cours sur la primitive de 1/x + +- Exercices: utilisation de la primitive de $\frac{1}{x}$ + +.. image:: ./Logarithme/Etude_fonction/3E_primitive.pdf + :height: 200px + :alt: Exercices sur la primitive de 1/x + Semaine 19: 4/05 -> 8/05 ========================