QUESTION 1 - 1 POINT A particle moves along a line with a velocity \( v(t)=t+8 \), measured in meters per second. Find the net displacement of the particle from time \( t=0 \) to time \( t=6 \). Enter an exact answer.

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

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.

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

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

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