Acceleration The velocity of an automobile starting from rest is \( v(t)=\frac{100 t}{2 t+15} \) where \( v \) is measured in feet per second and \( t \) is the time in seconds. Find the acceleration at (a) 5 seconds, (b) 10 seconds, and (c) 20 seconds.

(10 points) Use the Fundamental Theorem of Calculus to find the exact values of the definite integral. \( \int_{1}^{3} 3\left(2^{x}\right) d x= \)

4. (8 points) Calculate the following limit. Write DNE if the limit does not exist \( \lim _{x \rightarrow-1}\left(x^{2}-\frac{3 x}{x+2}\right)= \) 5. (16 points) Use the following phrases to complete the statements below to give

\begin{tabular}{|l|}\hline 2. Calcula el volumen \\ del sólido de \\ revolución que se \\ forma de girar sobre \\ el eje \( x \) la función \\ \( f(x)=x^{2}+x \) con \\ límites \( [-1,5] \)\end{tabular}

\( \operatorname { lx } _ { x \rightarrow 0 } = \sqrt { 1 + 3 x - 1 } \quad \lim \neq \frac { 0 } { 0 } \)

7. (8 points) Calculate the following limits. Write DNE if the limit does not exist. (a) \( \lim _{x \rightarrow 0^{+}} \frac{4}{x^{3}}= \) (b) \( \lim _{x \rightarrow 0^{-}} \frac{4}{x^{3}}= \) (c) \( \lim _{x \rightarrow 0} \frac{4}{x^{3}}= \) 8. ( 20 points) Suppose \( f \) and \( g \) are functions such that