A ball is thrown straight upward from the ground and attains a height of \( s(t)=-2 t^{2}+28 t+68 \mathrm{ft} \) above the ground after \( t \mathrm{sec} \). When does the ball reach the maximum height? What is the maximum height? a. The ball reaches the maximum height after 9 seconds; its maximum height is 302 ft.

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

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

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

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

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