Robert takes a roast out of the oven when the intemal temperature of the roast is \( 165^{\circ} \mathrm{F} \). After 15 minutes, the temperature of the roast drops to \( 135^{\circ} \mathrm{F} \). The temperature of the room is \( 70^{\circ} \mathrm{F} \). How long does it take for the temperature of the roast to drop to \( 110^{\circ} \mathrm{F} \) ? Use the Newton's Law of Cooling equation, \( T(t)=T_{A}+\left(T_{6}-T_{A}\right) \mathrm{e}^{\mathrm{k} t} \). Enter your answer in the box. Round your answer to the nearest minute. minutes

II. Dadas las funcione \( \mathrm{f}(\mathrm{x})=5 \mathrm{x}^{2}+4 \mathrm{x}-1 \) \( \mathrm{~g}(\mathrm{x})=\mathrm{x}^{2}-6 \) Encontra a) \( \operatorname{Lim}_{x \rightarrow 1}\left[\frac{f(x)}{g(x)}\right] \) b) \( \operatorname{Lim}_{x \rightarrow 0}[f(x) \cdot g(x)] \)

(2) \( f(x)=x^{3}-10 x^{2}-5 x+20 \) a) \( \int_{4}^{7} f(b)-f(a) \) b) \( 1^{\text {ra }} \) derivada c) Velocidad \( [5,8] \quad V_{m}=\frac{f\left(x_{f}\right)-f\left(x_{i}\right)}{V_{f}-x_{i}} \)

Use an appropriate test to determine whether the following series converges. \( \sum_{\mathrm{k}=1}^{\infty} \frac{5}{\sqrt{\mathrm{k}^{3}}} \) Select the correct choice below and fill in the answer box to complete your choice. A. The series diverges. It is a p-series with \( \mathrm{p}=\square \). The series converges. It is a p-series with \( \mathrm{p}=\square \). C. The series diverges by the Integral Test. The value of \( \int_{1}^{\infty} \frac{5}{\sqrt{\mathrm{x}^{3}}} \mathrm{dx} \) is \( \square \). D. The series converges by the Divergence Test. The value of \( \lim _{\mathrm{k} \rightarrow \infty} \frac{5}{\sqrt{\mathrm{k}^{3}}} \) is \( \square \). E. The series diverges by the Divergence Test. The value of \( \lim _{\mathrm{k} \rightarrow \infty} \frac{5}{\sqrt{\mathrm{k}^{3}}} \) is \( \square \).

Math 60 Exam \#4 1) Use Right-endpoint Rule with \( n=5 \) to approximate \( \int_{2}^{3} x \sqrt{x+1} d x \) to 4 decimal places.

\begin{tabular}{l} (1) \( f(x)=3 x^{3}+2 x^{2}-5 x-10 \) \\ a) \( \int_{3}^{8} f(b)-f(a)= \) \\ b) Derivada \\ c) Velocidad \( \quad{ }_{m}=\frac{f\left(x_{i}\right)-f(x i)}{x_{f}-x_{i}} \quad[3,5] \) \\ \hline\end{tabular}