EX_0215 – Soit $g$ la fonction définie sur $ $...

← EX_0215

Soit $g$ la fonction définie sur $ $ par $g(x)=-0,5x+3$

corrigé

Énoncé

Soit $g$ la fonction définie sur $\R$ par $g(x)=-0,5x+3$.
On définit alors la suite $v$ par $\sys{v_0=1}{v_{n+1}=g(v_n), \text{pour tout }n\in \N}$

Dans un repère orthonormé :
Conjecturer le sens de variation et la limite éventuelle de la suite $v$.

Correction

\begin{varwidth}{0.9\textwidth}
        \subsection*{Correction}
        \begin{enumerate}
            \item
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                    \psdots[dotsize=3pt 0,dotstyle=*,linecolor=uququq](1.,2.5)
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            \item On constate que $u_0<u_1$ mais que $u_1>u_2$ la suite ne semble ni croissante ni décroissante. Elle semble converger vers $2$ on conjecture donc que $\displaystyle \lim_{n\rightarrow +\infty}u_n=2$
        \end{enumerate}
    \end{varwidth}

Correction

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\psdots[dotsize=3pt 0,dotstyle=*,linecolor=uququq](1.,2.5) \psdots[dotsize=3pt 0,dotstyle=*,linecolor=uququq](0.,2.5) \rput[bl](-0.3538081560518486,2.459416267828339){\uququq{$U_1$}} \psdots[dotsize=3pt 0,dotstyle=*,linecolor=uququq](2.5,2.5) \psdots[dotsize=3pt 0,dotstyle=*,linecolor=uququq](2.5,0.) \psdots[dotsize=3pt 0,dotstyle=*,linecolor=uququq](2.5,1.75) \psdots[dotsize=3pt 0,dotstyle=*,linecolor=uququq](0.,1.75) \rput[bl](-0.3538081560518486,1.7231300715006879){\uququq{$U_2$}} \psdots[dotsize=3pt 0,dotstyle=*,linecolor=uququq](1.75,1.75) \psdots[dotsize=3pt 0,dotstyle=*,linecolor=uququq](1.75,0.) \psdots[dotsize=3pt 0,dotstyle=*,linecolor=uququq](1.75,2.125) \psdots[dotsize=3pt 0,dotstyle=*,linecolor=uququq](0.,2.125) \rput[bl](-0.3467959065630139,2.087767044920096){\uququq{$U_3$}} \psdots[dotsize=3pt 0,dotstyle=*,linecolor=uququq](2.125,2.125) \psdots[dotsize=3pt 0,dotstyle=*,linecolor=uququq](2.125,0.) \psdots[dotsize=3pt 0,dotstyle=*,linecolor=uququq](2.125,1.9375) \psdots[dotsize=3pt 0,dotstyle=*,linecolor=uququq](0.,1.9375) \rput[bl](-0.3467959065630139,1.8984363087215572){\uququq{$U_4$}} \psdots[dotsize=3pt 0,dotstyle=*,linecolor=uququq](1.9375,1.9375) \psdots[dotsize=3pt 0,dotstyle=*,linecolor=uququq](1.9375,0.)
On constate que $u_0u_2$ la suite ne semble ni croissante ni décroissante. Elle semble converger vers $2$ on conjecture donc que $\displaystyle \lim_{n\rightarrow +\infty}u_n=2$

Métadonnées

Identité

Titre

Niveau Statut

Type source Type tâche

Notes

Sources (1)

Année	Fichier	Barème
2022-2023	`DS\22-23\22-23-1spe-DS5.tex`	4 pts