Find the \( x \) and \( y \) coordinates of all inflection points. \( f(x)=x^{3}+15 x^{2} \) What is/are the inflection point(s)? Select the correct choice below and, if necessary, fill in the answer box to complete A. The inflection point(s) is/are (Type an ordered pair. Use a comma to separate answers as needed.) B. There are no inflection points.

\( \int _ { - \infty } ^ { \infty } x ^ { 4 } e ^ { - x ^ { 3 } } d x \)

Given that \( \int_{0}^{1}\left(2+3 \cos \frac{1}{2} x\right) d x=\int_{-1}^{2} e^{2 x+1} d x \), find the value of \( k \), giving your answer correct to 3 decimal places.

\( \lim _ { n \rightarrow \infty } [ \frac { 1 } { \sqrt { 4 n ^ { 2 } - 1 } } + \frac { 1 } { \sqrt { 4 n ^ { 2 } - 2 ^ { 2 } } } + \cdots + \frac { 1 } { \sqrt { 3 n ^ { 2 } } } ] \)

Find differenthal equation of the primitue \( x y+x^{2} y+y^{2}=13 \)

d) \( \lim _{n \rightarrow+\infty} \frac{\operatorname{sen}(1 / n)}{\operatorname{sen}(3 / n)} \)