\( f ( x ) = 2 x ^ { 3 } - 6 x , [ 0,3 ] \)

\begin{tabular}{|l|}\hline 3. \( \begin{array}{l}\text { Calcula el volumen } \\ \text { del sólido de } \\ \text { revolución que se } \\ \text { forma de girar sobre } \\ \text { el eje } x \text { las funciones } \\ f(x)=2 x^{2}+\frac{1}{2} y \\ g(x)=x \text { con límites } \\ {[0,3]}\end{array} \) \\ \hline\end{tabular}

\( \int _{}^{}\frac{dx}{x^{2}-8x-16} d \)

Calcule el limite de \( y=x^{2}+x-6 \) \( \lim _{x \rightarrow 3} \frac{x^{2}+x-6}{x+3} \)

38. Use integration formulas to solve each integral. You may have to use algebra, educated guess-and-check, and/or recognize an integrand as the result of a product, quotient, or chain rule calculation. (a) (10 points) \( \int\left(x^{2}-3 x^{8}-7\right) d x= \) (b) (10 points) \( \int 3 \cos (x) d x= \) (c) (10 points) \( \int x^{2}\left(x^{3}+1\right) d x= \)

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