QUESTION 1 - 1 POINT A particle moves along a line with a velocity \( v(t)=t+8 \), measured in meters per second. Find the net displacement of the particle from time \( t=0 \) to time \( t=6 \). Enter an exact answer.

Given that \( \int_{1}^{4} f(x) \mathrm{d} x=5 \), evaluate \( \begin{array}{ll}\text { (a) } \int_{4}^{1} 2 f(x) \mathrm{d} x, & \text { (b) } \int_{1}^{3} \mathrm{f}(x) \mathrm{d} x+\int_{3}^{4}[f(x)+3] \mathrm{d} x\end{array} \)

For each problem, approximate the area under the given function and above the \( x \)-axis on the give interval using the specified number of rectangles/trapezoids. You may use your calculator. 1.) \( f(x)=x^{2}-3 x+4,[1,4], n=6 \) a) Left Rectangles b) Right Rectangles c) Midpoint Rectangles d) Trapezoids

For each problem, approximate the area under the given function and above the \( x \)-axis on the given interval using the specified number of rectangles/trapezoids. You may use your calculator. 1.) \( f(x)=x^{2}-3 x+4,[1,4], n=6 \) a) Left Rectangles b) Right Rectangles c) Midpoint Rectangles d) Trapezoids (a)

Solt la fonction \( f \) définie ci-dessous: \[ f: x \mapsto(x+1) e^{-8 x+8} \] Déterminer la dérivée de \( f \).

Quelle estla dérivée de la fonction \( f \) ? Wh admettra qu'elle est dérivable sur chaque intervalle contenu dans son domaine de définition \( D=\mathbb{R} \) \[ f: x \mapsto \frac{1}{e^{x}+7} \]