Problem #$2$: VECTOR $-$ VALUED FUNCTIONS For the vector$-$valued function:

vec$(r)(t)=($:$sin(2t),3cos(4t),t$:$)$

carry out the following steps:

A$)$ Evaluate $\underset{t0}{lim}$vec$(r)(t)$ and $\underset{t}{lim}$vec$(r)(t),$ if each exist.

B$)$ Find vec$(r{)}^{\text{'}}(t)$ and evaluate vec$(r{)}^{\text{'}}(0).$

C$)$ Find vec$(r{)}^{\text{'}\text{'}}(t).$

D$)$ Evaluate ${\displaystyle \underset{\phantom{}}{\overset{\phantom{}}{}}}$vec$(r)(t)dt.$