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\dotfill +\end{itemize} + +\subsection*{Exemples de calculs} + +Calcul de la dérivée de $f(x) = 2x + 1 - 4\ln(x)$ +\afaire{} + +Calcul de la dérivée de $f(x) = (2x+1)\ln(x)$ +\afaire{} + + + + + +\end{document} diff --git a/TES/Logarithme/Etude_fonction/1E_derivation.pdf b/TES/Logarithme/Etude_fonction/1E_derivation.pdf new file mode 100644 index 0000000000000000000000000000000000000000..e3df3aa688f8f9d4f1a2b0a4498c6acf13907f7c GIT binary patch literal 59086 zcmce;Wo+i$vZftoW`+(kGbbH}C(O*u%*@Q`FmpQ0%*@Q3beI{Y-!rr4n@>8@%%8n2 z*|NRLOTJa*TFbi1CX@duM#n_Y217QxIJ64GO2kNHXJ`q-%L~Jx>|t+0#Gno^v@|ht zhG9^0F?9Z~Gh%j*HZTmr!glUNT8w|~nHc|T)q!F7r{%w{VuE3iHE?#c_-n!R*Wz#c zKij_+iY88WE{;YfPDE^f&nUt$$e7rgIhzwPu@U{R(**3Kr5L=0lq2F@lwO^ob} zOVVs;DO$=;c+}9Tnr{yW9cR_$4KY?#xOl*z+SIghMe{P-QZ^!=`37r2f30(g% z2~7Vu=ilN6rhi=ipYa0|^S@2Re=eAq{%z63{Ev_SGoE1n$Lar;aAIcp&x!aa3I2OT zu>a>o{1dtV77;A}JZ=99r+=kyW)7zRnZN(<>3d6E)@g$ssq0*ASG69ScvZ)nz;lds 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+\pagestyle{empty} +\geometry{left=10mm,right=10mm, top=10mm} + +\renewcommand{\baselinestretch}{0.8} + +\DeclareExerciseCollection{banque} +\xsimsetup{ + step=1, +} + +\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 new file mode 100644 index 0000000..4e45524 --- /dev/null +++ b/TES/Logarithme/Etude_fonction/banque.tex @@ -0,0 +1,38 @@ +\collectexercises{banque} +\begin{exercise}[subtitle={Éléments remarquables du logarithme}, step={1}, topics={Logarithme}] + \begin{enumerate} + \item Tracer l'allure de la courbe représentative du logarithme. + \item Repérer les éléments remarquables de cette représentation graphique. + \item Tracer le tableau de signe de $\ln$. + \item Tracer le tableau de variation de $\ln$. + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Dériver les fonctions}, step={1}, topics={Logarithme}] + Dériver les fonctions suivantes puis mettre sous une forme pratique pour l'étude de signe. + \begin{multicols}{3} + \begin{enumerate} + \item $f(x) = x-2-\ln(x)$ + \item $f(x) = 2x^2 - 2x + 4\ln(x)$ + \item $f(x) = x\ln(x)$ + \item $f(x) = (x+1)\ln(x)$ + \item $f(x) = (\ln(x) + 1)^2$ + \item(*) $f(x) = \frac{1 + \ln(x)}{x}$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{exercise}[subtitle={Dériver les fonctions - Bis}, step={1}, topics={Logarithme}] + Dériver les fonctions suivantes puis mettre sous une forme pratique pour l'étude de signe. + \begin{multicols}{3} + \begin{enumerate} + \item $f(x) = 2x - \ln(x) + 2$ + \item $f(x) = x^3 - 4\ln(x)$ + \item $f(x) = e^{3x} + 2 $ + \item $f(x) = (2x - 2)\ln(x)$ + \item(*) $f(x) = (\ln(x) + 1)(3x+2)$ + \item(*) $f(x) = \frac{\ln(x)}{x}$ + \end{enumerate} + \end{multicols} +\end{exercise} +\collectexercisesstop{banque} diff --git a/TES/Logarithme/Etude_fonction/index.rst b/TES/Logarithme/Etude_fonction/index.rst new file mode 100644 index 0000000..2359159 --- /dev/null +++ b/TES/Logarithme/Etude_fonction/index.rst @@ -0,0 +1,34 @@ +Étude de la fonction logarithme avec les TESL pour l'année 2019-2020 +#################################################################### + +:date: 2020-05-05 +:modified: 2020-05-05 +:authors: Bertrand Benjamin +:category: TESL +:tags: Logarithme +:summary: Étude de la fonction logarithme avec les TESL pour l'année 2019-2020 + + +Étape 1: Représentation graphique et dérivation +=============================================== + +Les élèves commencent par une étude graphique de la fonction ln pour noter les points remarquables. Puis ils notent le cours puis font les exercices techniques de dérivation. + +.. image:: 1E_derivation.pdf + :height: 200px + :alt: Exerices techniques de dérivation. + +Cours sur la représentation graphique du logarithme et les formules de dérivation. + +.. image:: 1B_definition_ln.pdf + :height: 200px + :alt: Bilan sur la définition et la dérivation du logarithme. + +Étape 2: Dérivation et étude de variations +========================================== + +Étape 3: Calculs d'aires +======================== + +Étape 4: Annales Bac +====================