96 lines
3.5 KiB
TeX
96 lines
3.5 KiB
TeX
\documentclass[a4paper,10pt]{article}
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\usepackage{myXsim}
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\usetikzlibrary{positioning}
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\author{Benjamin Bertrand}
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\title{Prolongement géométrique vers exponentiel - Exercices}
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\date{Décembre 2020}
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\DeclareExerciseCollection{banque}
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\xsimsetup{
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step=4,
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}
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\begin{document}
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\setcounter{section}{2}
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\section{Taux d'évolution moyen}
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\begin{definition}[Taux d'évolution moyen]
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\begin{minipage}{0.45\linewidth}
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On note $t_m$ le taux d'évolution et $T$ le taux d'évolution global et $n$ le nombre de 'sous-évolutions'. Alors
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\[
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1 + T = (1 + t_m)^n \qquad \qquad 1 + t_m = (1 + T)^{\frac{1}{n}}
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\]
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\end{minipage}
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\hfill
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\begin{minipage}{0.5\linewidth}
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\begin{tikzpicture}[
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roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
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node distance=2cm and 2cm
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]
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%Nodes
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\node[roundnode] (termA) {\makebox[0.5cm]{}};
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\node[roundnode] (termB) [right=of termA] {\makebox[0.5cm]{}};
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\node[roundnode] (termC) [right=of termB] {\makebox[0.5cm]{}};
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\node[roundnode] (termD) [right=of termC] {\makebox[0.5cm]{}};
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%Lines
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\path[->] (termA.north) edge [bend left] node [above] {$+t_m$} node [below] {$\times (1+t_m)$} (termB.north) ;
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\path[->] (termB.north) edge [bend left] node [above] {$+t_m$} node [below] {$\times (1+t_m)$} (termC.north) ;
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\path[->] (termC.north) edge [bend left] node [above] {$+t_m$} node [below] {$\times (1+t_m)$} (termD.north) ;
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\path[->] (termA.south) edge [bend right] node [above] {$+t_m$} node [below] {$\times (1+T)$} (termD.south);
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\end{tikzpicture}
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\end{minipage}
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\end{definition}
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\medskip
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\hline
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\input{exercises.tex}
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\printcollection{banque}
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\vfill
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\setcounter{section}{2}
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\section{Taux d'évolution moyen}
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\begin{definition}[Taux d'évolution moyen]
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\begin{minipage}{0.45\linewidth}
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On note $t_m$ le taux d'évolution et $T$ le taux d'évolution global et $n$ le nombre de 'sous-évolutions'. Alors
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\[
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1 + T = (1 + t_m)^n \qquad \qquad 1 + t_m = (1 + T)^{\frac{1}{n}}
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\]
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\end{minipage}
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\hfill
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\begin{minipage}{0.5\linewidth}
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\begin{tikzpicture}[
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roundnode/.style={circle, draw=highlightbg, fill=green!5, very thick, minimum size=3mm},
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node distance=2cm and 2cm
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]
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%Nodes
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\node[roundnode] (termA) {\makebox[0.5cm]{}};
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\node[roundnode] (termB) [right=of termA] {\makebox[0.5cm]{}};
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\node[roundnode] (termC) [right=of termB] {\makebox[0.5cm]{}};
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\node[roundnode] (termD) [right=of termC] {\makebox[0.5cm]{}};
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%Lines
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\path[->] (termA.north) edge [bend left] node [above] {$+t_m$} node [below] {$\times (1+t_m)$} (termB.north) ;
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\path[->] (termB.north) edge [bend left] node [above] {$+t_m$} node [below] {$\times (1+t_m)$} (termC.north) ;
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\path[->] (termC.north) edge [bend left] node [above] {$+t_m$} node [below] {$\times (1+t_m)$} (termD.north) ;
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\path[->] (termA.south) edge [bend right] node [above] {$+t_m$} node [below] {$\times (1+T)$} (termD.south);
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\end{tikzpicture}
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\end{minipage}
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\end{definition}
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\medskip
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\hline
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\printcollection{banque}
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\end{document}
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