\( \int _ { 0 } ^ { \pi / 3 } \sin ( x ) \cos ^ { 3 } ( x ) d x = \square \)

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.

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

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 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 \( \square \).

Use the given function to complete parts (a) through (e) below. \( f(x)=x^{4}-36 x^{2} \) 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. c) Find the \( y \)-intercept by computing \( f(0) \). (0) \( =\square \) d) Determine the symmetry of the graph. Odd; origin symmetry