\( \int _ { \frac { 5 } { \pi 10 ^ { 2 } } } ^ { \frac { \pi } { 5 ! } } \frac { e ^ { x + 3 } - 2 x ^ { 5 } + 4 e ^ { x ^ { 2 } } } { x ^ { 2 } - 6 } d [ x ] \)

3. Исследовать ряд на сходимость, используя радикальный признак Коши \[ \sum_{n=1}^{\infty}\left(\frac{8 n^{2}+4 n}{5 n+4 n^{2}}\right)^{n} \]

2. Вычислить пятую частичную сумму ряда \[ \sum_{n=1}^{\infty} \frac{(-1)^{n}(n+1)}{4 n} \]

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.)

Use the function below to answer parts a and \( \mathbf{b} \). \( f(x)=\frac{x^{3}}{3}-100 x \) on \( [-13,13] \) a. Find the critical points of the function on the given interval. The critical point(s) occur at \( x= \) (Simplify your answer. Use a comma to separate answers as needed. Type an exact answer, using radicals as needed.) b. Use a graphing utility to determine whether each critical point corresponds to a local maximum, local minimum, or neither. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The critical point(s) \( x=\square \) correspond(s) to the local maximum/maxima. (Simplify your answer. Use a comma to separate answers as needed. Type an exact answer, using radicals as needed.) There is no local maximum. Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The critical point(s) \( x=\square \) correspond(s) to the local minimum/minima. (Simplify your answer. Use a comma to separate answers as needed. Type an exact answer, using radicals as needed.) E. There is no local minimum.

\( \sum _ { n = 1 } ^ { \infty } \frac { ( - 1 ) ^ { n } ( n + 1 ) } { 4 n } \)