76 lines
2.5 KiB
TeX
76 lines
2.5 KiB
TeX
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\documentclass[a4paper,10pt]{article}
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\usepackage{myXsim}
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\title{Autour de la notion de continuité}
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\tribe{Terminale ES}
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\date{Septembre 2019}
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\pagestyle{empty}
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\begin{document}
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\begin{exercise}[subtitle={Toujours des solutions?}]
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Ci-dessous le graphiques de 3 fonctions définies sur $\intFF{-6}{5}$.
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\hspace{-1cm}
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\begin{minipage}{0.3\textwidth}
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\begin{tikzpicture}[baseline=(a.north), xscale=0.45, yscale=0.6]
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\tkzInit[xmin=-6,xmax=6,xstep=1,
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ymin=-3,ymax=3,ystep=1]
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\tkzGrid
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\tkzAxeXY
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\draw (4,2) node[below left] {$\mathcal{C}_g$};
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\tkzFct[domain = -6:6,color=red,very thick]%
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{0.05*(x+5)*(x+1)*(x-4)}
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\end{tikzpicture}
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\end{minipage}
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\hspace{0.5cm}
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\begin{minipage}{0.3\textwidth}
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\begin{tikzpicture}[baseline=(a.north), xscale=0.45, yscale=0.6]
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\tkzInit[xmin=-6,xmax=6,xstep=1,
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ymin=-3,ymax=3,ystep=1]
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\tkzGrid
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\tkzAxeXY
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\draw (4,2) node[above left] {$\mathcal{C}_g$};
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\tkzFct[domain = -6:6,color=red,very thick]%
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{2-exp(-0.25*x)}
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\end{tikzpicture}
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\end{minipage}
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\hspace{0.5cm}
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\begin{minipage}{0.3\textwidth}
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\begin{tikzpicture}[baseline=(a.north), xscale=0.45, yscale=0.6]
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\tkzInit[xmin=-6,xmax=6,xstep=1,
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ymin=-3,ymax=3,ystep=1]
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\tkzGrid
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\tkzAxeXY
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\draw (4,2) node[below left] {$\mathcal{C}_g$};
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\draw[very thick, color=red] plot [smooth,tension=0.5] coordinates{%
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(-6,-3) (-3,-2) (-2,-1)
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};
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\draw[very thick, color=red] plot [smooth,tension=0.5] coordinates{%
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(-2,0) (2, 0.5) (6,3)
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};
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\end{tikzpicture}
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\end{minipage}
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\begin{enumerate}
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\item Résoudre les équations suivantes pour chacune des fonctions.
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\begin{multicols}{3}
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\begin{enumerate}
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\item $g(x) = -1$ sur $\intFF{-6}{5}$
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\item $g(x) = 1$ sur $\intFF{-6}{5}$
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\item $g(x) = 1$ sur $\intFF{2}{5}$
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\end{enumerate}
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\end{multicols}
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\item Quelles conditions faut-il avoir sur une fonction $g$ et sur $a$ pour que l'équation $g(x)=a$ ait une solution?
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\item Même question mais pour que cette solution soit unique?
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\end{enumerate}
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\end{exercise}
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\vfill
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\printexercise{exercise}{1}
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\vfill
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\printexercise{exercise}{1}
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\vfill
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\end{document}
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