Derermine the values of the follow \( \begin{array}{ll}\int_{0}^{2}(2 x+1) d x & \text { b. } \int_{0}^{4} 2 x d x\end{array} \)

13. Find the derivative of the following function by first expanding the expression. \[ f(x)=(2 x+3)\left(3 x^{2}+1\right) \] \( f^{\prime}(x)=\square \)

14. Find the derivative of the function by first expanding the expression. \[ f(x)=(9 x+7)^{2} \] \( f^{\prime}(x)=\square \) 15. Find \( f^{\prime}(x), f^{\prime \prime}(x) \), and \( f^{(3)}(x) \) for the following function.

3. Evaluate the following limit. \( \lim _{x \rightarrow-1} \frac{x^{2}-1}{x+1} \) Rewrite the given limit in a way that can be evaluated by direct substitution. \( \lim _{x \rightarrow-1} \frac{x^{2}-1}{x+1}=\lim _{x \rightarrow-1} \) (Simplify your answer.) \( \lim _{x \rightarrow-1} \frac{x^{2}-1}{x+1}=\square \) (Type an exact answer.)

Find the limit of the polynomial \( p(x) \) as \( x \) approaches \( -\infty \) \[ p(x)=4 x^{7}-7 x^{6}+1 \] The limit of \( p(x) \) as \( x \) approaches \( -\infty \) is

17. Consider the following cost function. a. Find the average cost and marginal cost functions. b. Determine the average and marginal cost when \( x=a \). c. Interpret the values obtained in part (b). \( C(x)=1200+0.2 x, 0 \leq x \leq 5000, a=2800 \) a. The average cost function is \( \overline{\mathrm{C}}(\mathrm{x})=\square \) The marginal cost function is \( \mathrm{C}^{\prime}(\mathrm{x})=\square \) b. The average cost when \( x=2800 \) is \( \$ \square \). The marginal cost when \( x=2800 \) is \( \$ \square \). c. The average cost per item is about \( \$ \square \) to two decimal places as needed.) (Round to two decimal places as needed.) The cost of producing the two decimal places as needed.) (Round to two decimal places as needed.)