151 lines
4.6 KiB
TeX
151 lines
4.6 KiB
TeX
\documentclass[a4paper,10pt,xcolor=table]{classPres}
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%\usepackage{myXsim}
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% Title Page
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\title{Croissance - Exercices}
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% \tribe{Terminale ES}
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\date{Septembre 2019}
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\begin{document}
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\begin{frame}{Petite zoologie des suites}
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\begin{columns}
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\begin{column}[t]{0.5\textwidth}
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\textbf{Suite Arithmétique}
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\[
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u_n \xrightarrow{+r} u_{n+1}
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\]
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\begin{itemize}
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\item Récurrence $u_{n+1} = u_n + r$
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\item Explicite $u_n = u_0 + n\times r$
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\end{itemize}
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\end{column}
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\begin{column}[t]{0.5\textwidth}
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\textbf{Suite Géométrique}
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\[
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u_n \xrightarrow{\times q} u_{n+1}
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\]
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\begin{itemize}
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\item Récurrence $u_{n+1} = u_n \times q$
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\item Explicite $u_n = u_0 \times q^n$
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\end{itemize}
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\end{column}
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\end{columns}
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\vfill
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\pause
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\begin{block}{Variations}
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\begin{itemize}
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\item À quelle condition une suite arithmétique est croissante?
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\item À quelle condition une suite géométrique est croissante?
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\end{itemize}
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\end{block}
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\end{frame}
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\begin{frame}{Variations d'une suite arithmétique}
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\framesubtitle{$(u_n)$ arithmétique de raison $r$}
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\begin{columns}
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\begin{column}[t]{0.5\textwidth}
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Si $r > 0$, $(u_n)$ est croissante
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\begin{center}
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\begin{tikzpicture}[scale=0.4]
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\filldraw[very thick, ->] (-0.4,0) -- (6.4,0);
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\filldraw[very thick, ->] (0,-0.4) -- (0,4.4);
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\foreach \x in {0,...,5}{%
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\draw (\x, 1+0.5*\x) node {x};
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}
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\end{tikzpicture}
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\end{center}
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\end{column}
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\begin{column}[t]{0.5\textwidth}
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Si $r < 0$, $(u_n)$ est décroissante
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\begin{center}
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\begin{tikzpicture}[scale=0.4]
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\filldraw[very thick, ->] (-0.4,0) -- (6.4,0);
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\filldraw[very thick, ->] (0,-0.4) -- (0,4.4);
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\foreach \x in {0,...,5}{%
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\draw (\x, 3.5-0.5*\x) node {x};
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}
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\end{tikzpicture}
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\end{center}
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\end{column}
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\end{columns}
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\pause
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\begin{block}{Démonstration}
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\vfill
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\end{block}
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\vfill
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\end{frame}
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\begin{frame}{Variations d'une suite géométrique}
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\framesubtitle{$(u_n)$ géométrique de raison $q$}
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\begin{block}{Si $u_0 > 0$}
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\begin{columns}
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\begin{column}[t]{0.5\textwidth}
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Si $q > 1$, $(u_n)$ est croissante
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\begin{center}
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\begin{tikzpicture}[scale=0.4]
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\filldraw[very thick, ->] (-0.4,0) -- (6.4,0);
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\filldraw[very thick, ->] (0,-0.4) -- (0,4.4);
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\foreach \x in {0,...,5}{%
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\draw (\x, 0.1*2^\x) node {x};
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}
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\end{tikzpicture}
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\end{center}
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\end{column}
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\begin{column}[t]{0.5\textwidth}
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Si $0 < q < 1$, $(u_n)$ est décroissante
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\begin{center}
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\begin{tikzpicture}[scale=0.4]
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\filldraw[very thick, ->] (-0.4,0) -- (6.4,0);
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\filldraw[very thick, ->] (0,-0.4) -- (0,4.6);
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\foreach \x in {0,...,5}{%
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\draw (\x, 4*0.5^\x) node {x};
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}
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\end{tikzpicture}
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\end{center}
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\end{column}
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\end{columns}
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\end{block}
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\pause
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\begin{block}{Si $u_0 < 0$}
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\begin{columns}
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\begin{column}[t]{0.5\textwidth}
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Si $q > 1$, $(u_n)$ est croissante
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\begin{center}
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\begin{tikzpicture}[scale=0.4]
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\filldraw[very thick, ->] (-0.4,0) -- (6.4,0);
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\filldraw[very thick, ->] (0,-4.4) -- (0,0.6);
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\foreach \x in {0,...,5}{%
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\draw (\x, -0.1*2^\x) node {x};
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}
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\end{tikzpicture}
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\end{center}
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\end{column}
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\begin{column}[t]{0.5\textwidth}
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Si $0 < q < 1$, $(u_n)$ est décroissante
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\begin{center}
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\begin{tikzpicture}[scale=0.4]
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\filldraw[very thick, ->] (-0.4,0) -- (6.4,0);
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\filldraw[very thick, ->] (0,-4.4) -- (0,0.6);
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\foreach \x in {0,...,5}{%
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\draw (\x, -4*0.5^\x) node {x};
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}
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\end{tikzpicture}
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\end{center}
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\end{column}
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\end{columns}
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\end{block}
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\pause
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\begin{block}{Démonstration}
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\end{block}
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\end{frame}
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\end{document}
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