Funcion de transferencia \( \begin{array}{ll}m x^{\prime \prime}+b x^{\prime}+k x=0 & x(0)=1 \\ m=1 k g \quad b=5 \quad k=4 & v_{0}=0\end{array} \)

Use the given function to complete parts (a) through (e) below. \( f(x)=x^{4}-36 x^{2} \) c) Find the \( y \)-intercept by computing \( f(0) \). \( f(0)= \) d) Determine the symmetry of the graph. Odd; origin symmetry Even; \( y \)-axis symmetry Neither

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.

\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}

(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 \( \square \).