Consider the LTI system characterized by I$/$O relationship

$y(t)={\displaystyle \underset{t-4}{\overset{t}{}}}{e}^{-3(t-)}x()d$

$($a$)(10$pts$)$ What is the impulse response of the system?

$($b$)(5$pts$)$ Is this system, $h(t),$ causal? Justify your answer.

$($c$)(10$pts$)$ Assume $x(t)=e^{-2t}u(t).$ Determine a closed$-$form expression for the output $y(t).$

HINT$1$: ${\displaystyle \underset{a}{\overset{b}{}}}f()d={\displaystyle \underset{-}{\overset{}{}}}f()[u(b-)-u(a-)]d.$

HINT$2$: Remember a system is Causal if $h(t)=0$ for all

HINT$3$: You may use the following formula:

$e^{at}u(t)**e^{bt}u(t)=\frac{1}{a-b}{e}^{at}u(t)+\frac{1}{b-a}{e}^{bt}u(t)$