16. ( 3 points) The position of a particle on a line is given by \( s(t)=-3 t^{2}+6 t+5 \) where \( t \) is measured in seconds and \( s \) is measured in feet. Find the speed of the psrticle when \( t=2 \) seconds. \( \begin{array}{ll}\text { (A) }-6 \mathrm{ft} / \mathrm{s} & \text { (B) } 6 \mathrm{ft} / \mathrm{s} \\ \text { (C) }-1 \mathrm{ft} / \mathrm{s} & \text { (D) } 5 \mathrm{ft} / \mathrm{s}\end{array} \)

47) \( D_{x} \operatorname{sen}(3 x-2)= \)

144 Limite d'une suite Déterminer les limites des suites suivantes. a) \( \left(u_{n}\right) \) définie par \( u_{n}=\left(2 n+n^{2}\right) \times \sqrt{n} \). b) \( \left(v_{n}\right) \) définie par \( v_{n}=\frac{3 n^{2}+5}{2 n^{2}-4} \). c) \( \left(w_{n}\right) \) définie par \( w_{n}=n^{2}+(-1)^{n} \). d) \( \left(a_{n}\right) \) définie par \( a_{n}=3+\frac{\cos (3 n+1)}{n^{3}} \). e) \( \left(b_{n}\right) \), qui est la suite géométrique de raison \( \frac{1}{4} \) et de premier terme \( b_{0}=10 \) f) \( \left(c_{n}\right) \) définie par \( c_{n}=-4 \times 2^{n} \)

(a) Let \( f \) be a continuous function on \( [0,1] \) and differentiable on \( (0,1) \). Let also \( f(0)= \) \( f(1)=0 \). Prove that there exists a point \( c \in(0,1) \) such that \( f^{\prime}(c)=f(c) \). (Hint use \( \left.g(x)=f(x) e^{-x}\right) \). (b) If \( f^{\prime}(x)=0 \) at each point in an open interval \( (a, b) \). Prove that \( f \) is a constant on the interval \( (a, b) \). (c) Show that the equation \( \cos x=x \) has a root between 0 and 1 . (cos,\( =0 \) (d) Where is \( f(x)=x e^{2 x} \) increasing or decreasing?

b. (4 points) \( g(x)=4^{-x} \cdot \sin (x)+\ln \left(e^{x}+e^{-x}\right)+e^{2} \)

DIketahui \( D=\frac{18}{4} r^{3} \hat{a}_{r} \) dimana \( r \leq 5 \leq 2 m ; 0 \leq z \leq 10 ; 0 \leq \varphi \leq 2 \pi \) Tunjukan ruas kiri dan kanan dari teorema divergensi \( \int / \vec{D} \cdot \overrightarrow{d s}=\iint / \nabla \cdot D \cdot d v \)