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zaq^Xjb~aDR&%|DCO?52IhJ+n@^X(kXZ}2)yOb{9&1_Nnj2a(vUh9mFDU0(AB$t2Zz zQ}osj*pBzAyi<2*z+)$ev}UkS0C|ATy}u6XfI-@WFT*YQ3=Q)mpV>oS;FN6(5dUwsB{P66MV=Rw49Knz$E0fg%bbK6@Gl)olSG%9 zgq4K(Us1)u!S!G9|NQHt0>>n6Z{hGy{X?<-qr^yb`NY@&TpY}tq9QE9VyyofIhk3- zg}MHvNr|wCv9U>T2$1~$Tl5kB3we>SaBwD|g3$sA=cHM{g>XXlu4l}~#bDyXP*j70 zNCx?kd3DvRh1&c~50S>_VKaOCA?g3tI|ZFS@9;f#Ek#_FCnugu7K&kF8O;?&YOz#s zV%}{m$Spr&GK&*=i&GZ8`y-fFd0ML=xP-(7EFPhZwJ8U^oRGC_2 zR;3W_(q01kK9))$M2$Qon_B3LS%A9WXLRw|*V; H3Aq0OHh(|r diff --git a/TST_sti2d/DS/DS_20_11_12/DS_20_11_12.tex b/TST_sti2d/DS/DS_20_11_12/DS_20_11_12.tex index b4fe99b..db27c55 100644 --- a/TST_sti2d/DS/DS_20_11_12/DS_20_11_12.tex +++ b/TST_sti2d/DS/DS_20_11_12/DS_20_11_12.tex @@ -17,8 +17,8 @@ Le barème est donné à titre indicatif, il pourra être modifié. \begin{exercise}[subtitle={Automatismes}, points=5] Dans cet exercice les questions sont indépendantes. \begin{enumerate} - \item Dériver, en détaillant les étapes, la fonction $f(x) = \cos(x) (-3x + 10)$ - \item Soit $g(x) = x^2 + 1$. Calculer le taux de variation $\dfrac{\Delta g}{\Delta x}$ entre $x_1 = 1$ et $x_2 = 4$. + \item Dériver, en détaillant les étapes, la fonction $f(x) = \cos(x) (1 - 4x)$ + \item Soit $g(x) = x^2 + 1$. Calculer le taux de variation $\dfrac{\Delta g}{\Delta x}$ entre $x_1 = -1$ et $x_2 = 4$. \item Tracer puis donner l'équation de la tangente au point $x=1$ dans la courbe suivante \begin{tikzpicture}[baseline=(a.north), xscale=2.5, yscale=1.5] @@ -29,17 +29,17 @@ Le barème est donné à titre indicatif, il pourra être modifié. \tkzFct[domain = 0:5,color=red,very thick]% {2*exp(0.5)*x*exp(-0.5*x**2)}; \end{tikzpicture} - \item La loi des gaz parfait s'écrit $PV = nRT$ exprimer $T$ en fonction des autres paramètres. - \item Quelle est la valeur exacte de $\cos(\dfrac{-2\pi}{3})$? Justifier votre réponse. + \item La loi des gaz parfait s'écrit $PV = nRT$ exprimer $R$ en fonction des autres paramètres. + \item Quelle est la valeur exacte de $\cos(\dfrac{-5\pi}{6})$? Justifier votre réponse. \end{enumerate} \end{exercise} \vfill \begin{exercise}[subtitle={Citerne}, points=6] Soit $f$ la fonction définie sur $\R$ par - \[ f(t) = 2.5^4 - 4t^3 + 2.5t^2 - 6t + 10\] + \[ f(t) = 5^4 - 8t^3 + 2.5t^2 - 6t + 10\] \begin{enumerate} - \item Calculer $f'(t)$ puis en déduire que $f'(t) = (2t^2+1)(5t-6)$. + \item Calculer $f'(t)$ puis en déduire que $f'(t) = (4t^2+1)(5t-6)$. \item Étudier le signe de $f'(t)$ et en déduire les variations de $f(t)$. \item La fonction $f$ a-t-elle un maximum? Un minimum? Quelle est alors sa valeur? \end{enumerate} @@ -53,13 +53,13 @@ Le barème est donné à titre indicatif, il pourra être modifié. On note $z_A$, $z_B$ et $z_C$ les nombres complexes suivants \[ - z_A = -2 - 2i \qquad \qquad z_B = 2i + 4 \qquad \qquad z_C = -1 + \sqrt{3}i + z_A = -2 - 3i \qquad \qquad z_B = 3i + 4 \qquad \qquad z_C = 1 - \sqrt{3}i \] \begin{enumerate} \item Calculer le conjugué de $z_A$ \item Calculer les quantités suivantes \[ - z_D = z_A + z_B \qquad z_E = z_B \times z_A \qquad z_F = \frac{z_A}{z_B} + z_D = z_A + z_B \qquad z_E = z_B \times z_A \qquad z_F = \frac{z_B}{z_A} \] \item Calculer le module et l'argument de $z_C$. \item Soit $Z$ le nombre complexe de module $r = 3$ et d'argument $\theta = \dfrac{2\pi}{3}$. Donner la forme algébrique de $Z$.