Use an appropriate test to determine whether the following series converges. \( \sum_{\mathrm{k}=1}^{\infty} \frac{1}{\sqrt[3]{\mathrm{k}}} \) Select the correct choice below and fill in the answer box to complete your choice. (Simplify your answer.)

\( \lim _ { x \rightarrow 0 } ( \frac { a - \cos ( \underline { 3 } x ) } { x - \sin ( b x ) } ) = ? \)

(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 \( [5,8] \quad V_{m}=\frac{f\left(x_{f}\right)-f\left(x_{i}\right)}{V_{f}-x_{i}} \)

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) \( \operatorname{Lim}_{x \rightarrow 0}[f(x) \cdot g(x)] \)

Use the given function to complete parts (a) through (e) below. \( f(x)=x^{4}-36 x^{2} \) At which zeros does the graph of the function touch the \( x \)-axis and turn around? Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( x=\square \) (Type an integer or a decimal. Use a comma to separate answers as needed.) B. There are no \( x \)-intercepts at which the graph touches the \( x \)-axis and turns around.

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.