From 854490225ebd678594183bc2a58e8e6088f39bbd Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Mon, 3 Jan 2022 10:32:20 +0100 Subject: [PATCH] =?UTF-8?q?Feat:=20d=C3=A9but=20du=20chapitre=20sur=20les?= =?UTF-8?q?=20tableaux?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- 2nd/09_Fonctions_tableaux/1B.tex | 14 --- 2nd/09_Fonctions_tableaux/1B_tableaux.pdf | Bin 0 -> 45742 bytes 2nd/09_Fonctions_tableaux/1B_tableaux.tex | 81 ++++++++++++++++++ 2nd/09_Fonctions_tableaux/2B_variations.pdf | Bin 0 -> 24672 bytes 2nd/09_Fonctions_tableaux/2B_variations.tex | 50 +++++++++++ .../2E_tracer_tableau.pdf | Bin 0 -> 67592 bytes .../2E_tracer_tableau.tex | 29 +++++++ 2nd/09_Fonctions_tableaux/exercises.tex | 63 ++++++++++++-- 2nd/09_Fonctions_tableaux/index.rst | 12 ++- 9 files changed, 229 insertions(+), 20 deletions(-) delete mode 100644 2nd/09_Fonctions_tableaux/1B.tex create mode 100644 2nd/09_Fonctions_tableaux/1B_tableaux.pdf create mode 100644 2nd/09_Fonctions_tableaux/1B_tableaux.tex create mode 100644 2nd/09_Fonctions_tableaux/2B_variations.pdf create mode 100644 2nd/09_Fonctions_tableaux/2B_variations.tex create mode 100644 2nd/09_Fonctions_tableaux/2E_tracer_tableau.pdf create mode 100644 2nd/09_Fonctions_tableaux/2E_tracer_tableau.tex diff --git a/2nd/09_Fonctions_tableaux/1B.tex b/2nd/09_Fonctions_tableaux/1B.tex deleted file mode 100644 index 194a070..0000000 --- a/2nd/09_Fonctions_tableaux/1B.tex +++ /dev/null @@ -1,14 +0,0 @@ -\documentclass[a4paper,10pt]{article} -\usepackage{myXsim} - -\author{Benjamin Bertrand} -\title{Fonctions tableaux - Cours} -\date{2021-10-18} - -\pagestyle{empty} - -\begin{document} - -\maketitle - -\end{document} diff --git a/2nd/09_Fonctions_tableaux/1B_tableaux.pdf b/2nd/09_Fonctions_tableaux/1B_tableaux.pdf new file mode 100644 index 0000000000000000000000000000000000000000..5a444bfe91c2c76a71dcacdb14426eecfde7c583 GIT binary patch literal 45742 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des fonctions que nous identifiés lors de la séance "Qui est-ce?" sur les fonctions: \textbf{le signe} et \textbf{les variations}. + +\section{Tableaux de signes} + +Ce type de tableau représentera uniquement le \textbf{signe} de la fonction ainsi que les valeurs où elle est \textbf{nulle}. + +\paragraph{Exemple}: + +\begin{minipage}{0.5\linewidth} + \begin{tikzpicture} + % {0.1*(x+4)*(x+1)*(x-5)} + \begin{axis}[ + axis lines = center, + %grid = both, + xlabel = {$x$}, + xtick distance=1, + ylabel = {$y$}, + ytick distance=1, + legend pos = north west, + legend entries={$f(x)$} + ] + \addplot[domain=-6:6,samples=40, color=red, very thick]{0.1*(x+4)*(x+1)*(x-5)}; + \end{axis} + \end{tikzpicture} +\end{minipage} +\begin{minipage}{0.5\linewidth} + Tableau de signe de la fonction $f$ + + \vspace{4cm} + +\end{minipage} + +\section{Tableaux de variations} + +Ce type de tableau représentera uniquement les \texbf{variations} de la fonctions. + +\paragraph{Exemple}: + +\begin{minipage}{0.5\linewidth} + \begin{tikzpicture} + % x sin(2x) + \begin{axis}[ + axis lines = center, + %grid = both, + xlabel = {$x$}, + xtick distance=1, + ylabel = {$y$}, + ytick distance=1, + legend pos = north west, + ] + \addplot[domain=-6:6,samples=40, color=red, very thick]{x*sin(deg(x))}; + \end{axis} + \end{tikzpicture} + +\end{minipage} +\begin{minipage}{0.5\linewidth} + Tableau de variations de la fonction $f$ + + \vspace{4cm} +\end{minipage} + +\end{document} diff --git a/2nd/09_Fonctions_tableaux/2B_variations.pdf b/2nd/09_Fonctions_tableaux/2B_variations.pdf new file mode 100644 index 0000000000000000000000000000000000000000..5c17bcf03072378522e2dd017f9d6f3f18126dad GIT binary patch literal 24672 zcmce-W2`W3vnIN1+qP}nwr$(C^(@=ZvTfV8ZF`;f+cV#seKIGR`Lp+(bmvBOrLRx#mVv?3dVmZ{yG2G{T~V?Q)hcu zCu37*0@iVUZjIvAu~Y6dxayvx}3d zp)Hih#v=TT0>#W85CHf$;2o5yoyq?^`Dga8S7-l+@qZ5lj{hnMod0bQ82=@l{}M4U z{!8TlJ#t`V`Y!|V-=|EB|7F_5^e-9z_eg^2Uqb&cQ70zm|2`1^GJ^j#AlUxSN{ 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b/2nd/09_Fonctions_tableaux/2B_variations.tex new file mode 100644 index 0000000..2890f17 --- /dev/null +++ b/2nd/09_Fonctions_tableaux/2B_variations.tex @@ -0,0 +1,50 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} +\usepackage{pgfplots} +\pgfplotsset{compat = newest} +\usepgfplotslibrary{external} +\tikzexternalize + +\author{Benjamin Bertrand} +\title{Fonctions tableaux - Cours \hfill (suite)} +\date{2021-10-18} + +\pagestyle{empty} + +\begin{document} + +\maketitle + +\bigskip + +\setcounter{section}{2} +\section{Les variations d'une fonction} + +\begin{definition}[ variations d'une fonction ] + Soit $f$ une fonction définie sur un intervalle $I$. + + \medskip + + \begin{minipage}{0.5\linewidth} + On dit que $f$ est \textbf{croissante} sur $I$ si et seulement \dotfill + \medskip + \\.\dotfill + \medskip + \end{minipage} + \begin{minipage}{0.5\linewidth} + + \end{minipage} + + \begin{minipage}{0.5\linewidth} + On dit que $f$ est \textbf{décroissante} sur $I$ si et seulement \dotfill + \medskip + \\.\dotfill + \medskip + \end{minipage} + \begin{minipage}{0.5\linewidth} + + \end{minipage} + +\end{definition} + +\end{document} diff --git a/2nd/09_Fonctions_tableaux/2E_tracer_tableau.pdf b/2nd/09_Fonctions_tableaux/2E_tracer_tableau.pdf new file mode 100644 index 0000000000000000000000000000000000000000..1b303c31e5b84d7648fdcb57ef3a4cc88bde651c GIT binary patch literal 67592 zcmcfIb8uzN{wVwjCKKDXlO5Z(ZQC{`_QbYrn-kl{#1q?ZX3led@4dHf)&1+7RPF4w zSASRU?&?l=`m+E1??1<0&c}4*eAZ2W0>STsb&y4@i&u1>?R!+ta_y7?reJ5ifV?$dbV@Mtz zNJl3JV|{B#x79hgNjdV#ZQw88-heJ4jcttnN%=hbQ*_qPjQ=}TVEa#1f&IT$1^PdY z^B-vj`aezn-)RSWhW}V4{(GH?{y)~682+^Jf2SoF{xtf3q&qP%{`V^JXAu0)RD$Kd zSBXD8_dikz#y@{;|L#uz9=_?>8R`EH;Q#O8d%=684u{=gKTFr%m2jbrV7xz%bweRB zRV9yMqM>B|`^0!f0Y-equAK7Q!`U}MJ#eAzAs7|SQKiwJA%{DDc;h|(ob7K{LpI&M zz0cWDs#zmgnhmoVK5PVy9o~7}(I3}%-M&}dUA|XS-HO*kPrHq%%@@915Y1x7Hqj%( zoIWq_KiBYd-cPr5AfB#^Wvg4fpYAu-R1fxLtIzwclV2Bny+3Rd>YGH^6|9JpP2Mo- za6iJX-#Gv*6VH*UCkwJkVeHWE9G`yLJaBqh3i8z 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z2;bLlmHsJg8oMrSJS9xXpo>Cy9jr&-q@Fk5*ip#Pv@EdKuY$dra4sk7G}YJOxn z6PUtq%u}ISbP%}ea-$_;p&!r!)ZVOh+?c7eM$>+>n4FOv#~>Xt0aM(WJI&wik&SF= zu#kf@_vpk%9WZ^0tJ0vN{sH{zDxUv80G1qnbCQ!8EHb%y7c$##0>@3<) zw2I~)#=m<|w5oWT^mvST^uNaxY;B$J*#A?Vs_>t16I;ChhMNA<5W>^s66R;)7Zzj| zV4)LWV4!Ca5EiBv5@r)(qoZdM6r|^;=fV5Ghx|T8%Gk#A7dkO8{f|mky#L?^E2m#D zLn~tSiPj?b#&5qaB};FnoumPbnNU<#Kgj~B2fPy#Y}, step={1}, origin={<++>}, topics={ Fonctions tableaux }, tags={ Fonctions }] - <++> +\begin{exercise}[subtitle={Tableaux pour décrire les fonctions}, step={2}, origin={Création}, topics={Dérivation}, tags={Tableaux de signes, Tableaux de variations}] + \begin{minipage}{0.5\textwidth} + + Ci-contre, le graphique d'une fonction. + + \begin{enumerate} + \item Décrire ce graphique avec un tableau de signes. + \item Décrire ce graphique avec un tableau de variations. + \item (*) Décrire votre méthode pour construire un tableau de signes à partir du graphique. + \item (*) Décrire votre méthode pour construire un tableau de variations à partir du graphique. + \end{enumerate} + + \end{minipage} + \begin{minipage}{0.5\textwidth} + \begin{tikzpicture}[baseline=(a.north), xscale=0.8, yscale=0.45] + \tkzInit[xmin=-5,xmax=5,xstep=1, + ymin=-5,ymax=3,ystep=1] + \tkzGrid + \tkzAxeXY + \draw (-4, 1) node [above left] {$\mathcal{C}_f$}; + \draw [color=red, very thick] plot [smooth] coordinates {(-5,1) (-4,0) (-3, -3) (-2, -1) (-1, -3) (0, -4) (1, -2.5) (2, 0) (3, 1) (4, 0) (5, 2) }; + \end{tikzpicture} + \end{minipage} \end{exercise} -\begin{solution} - <++> -\end{solution} +\begin{exercise}[subtitle={Faire des tableaux}, step={2}, origin={Création}, topics={Dérivation}, tags={Tableaux de signes, Tableaux de variations}] + Pour toutes les fonctions ci-dessous, tracer le tableau de signes puis le tableau de variations. + + \begin{multicols}{2} + \begin{enumerate} + \item + \begin{tikzpicture}[baseline=(a.north), xscale=0.7, yscale=0.5] + \tkzInit[xmin=-5,xmax=5,xstep=1, + ymin=-5,ymax=3,ystep=1] + \tkzGrid + \tkzAxeXY + \draw [color=red, very thick] plot [smooth] coordinates {(-5,2) (-4,-2) (-3, -3) (-2, -2) (-1, 0) (0, 0) (1, -2.5) (2, 0) (3, 2) (4, 1) (5, 2) }; + \draw (-4, 1) node [above left] {$\mathcal{C}_f$}; + \end{tikzpicture} + \item $h(x) = x^3 - 2x + 1$ + \columnbreak + \item + \begin{tikzpicture} + % x sin(2x) + \begin{axis}[ + axis lines = center, + %grid = both, + xlabel = {$x$}, + xtick distance=1, + ylabel = {$y$}, + ytick distance=1, + legend pos = north west, + ] + \addplot[domain=-6:6,samples=80, color=red, very thick]{x*cos(deg(x)*pi/2)}; + \end{axis} + \end{tikzpicture} + \item $i(x) = -2(x-2)(x+1)(x+2)$ + \end{enumerate} + \end{multicols} +\end{exercise} diff --git a/2nd/09_Fonctions_tableaux/index.rst b/2nd/09_Fonctions_tableaux/index.rst index bba3f3d..4845ac1 100644 --- a/2nd/09_Fonctions_tableaux/index.rst +++ b/2nd/09_Fonctions_tableaux/index.rst @@ -2,7 +2,7 @@ Fonctions tableaux ################## :date: 2021-10-18 -:modified: 2021-12-14 +:modified: 2022-01-03 :authors: Benjamin Bertrand :tags: Fonctions :category: 2nd @@ -26,9 +26,19 @@ On espère que sorte la notion de signe d'une fonction et de variations. Ce qui Bilan: Des exemples de tableaux de signe et de variations +.. image:: ./1B_tableaux.pdf + :height: 200px + :alt: + + Étape 2: Tracer des tableaux ============================ +.. image:: ./2E_tracer_tableau.pdf + :height: 200px + :alt: + + A partir de graphique et de fonctions (à tracer avec la calculatrice) les élèves doivent tracer les tableaux. Étape 3: Raisonner sur des tableaux