2. (50 points) The population of Smallboro is estimated to be \[ p(t)=20-\frac{6}{t+1} \] thousand residents, \( t \) years from now. An environmental consultant shows that the level of carbon monoxide in the air is \[ c(x)=0.5 \cdot\left(x^{2}+x+58\right)^{0.5} \] \( \mathrm{ppm}^{\prime} \) (parts per million) when the population is \( x \) thousand people. (a) Express the amount of carbon monoxide in the air as a function of time (b) Will carbon monoxide levels be increasing or decreasing 2 years from now? At what rate? Make sure to state the correct units.

4. (8 points) Calculate the following limit. Write DNE if the limit does not exist \( \lim _{x \rightarrow-1}\left(x^{2}-\frac{3 x}{x+2}\right)= \) 5. (16 points) Use the following phrases to complete the statements below to give

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

\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}

(10 points) Use the Fundamental Theorem of Calculus to find the exact values of the definite integral. \( \int_{1}^{3} 3\left(2^{x}\right) d x= \)

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