Let $r(t)=(1-t^2)hat(i)+t{e}^{-t}$hat$(j)+(t+3)hat(k).$

a$)$ What is $\underset{t}{lim}r(t)?$

b$)$ What is $\frac{dr}{dt}?$

c$)$ What is ${\displaystyle \underset{0}{\overset{5}{}}}r(t)dt?$

Let $r(t)=($:$2tcos(t),5,(t-t^2)e^t$:$).$

a$)$ What is $\frac{dr}{dt}?$

b$)$ What is ${\displaystyle \underset{\frac{}{4}}{\overset{}{}}}r(t)dt?$