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.

Find the following indefinite integral \[ \int 9 x^{2} d x \]

Solve the differential equation \( \frac{dy}{dx} = 6y \) using separation of variables.

2. \( \left\{x_{n}\right\} \) ketma-ketlikning yuqori va quyi limitlari topilsin. \( x_{n}=\left(1+\frac{1}{n}\right)^{n}(-1)^{n}+\sin \frac{n \pi}{4} \) 3. Limit hisoblansin. \( \lim \left(\sqrt{1+x+x^{2}}-\sqrt{1-x+x^{2}}\right) \)

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.

\( \lim _ { m \rightarrow + \infty } \frac { t ^ { 2 } ( 1 | n ) } { 1 - \cos ( 1 / m ) } \)