Determine whether the given improper integral converges or diverges.

$($a$)$ If convergent, evaluate the integral and give the numerical answer.

$($b$)$ If divergent, indicate if the integral diverges to positive or negative infinity.

${\displaystyle \underset{-2}{\overset{}{}}}{e}^{-3x}dx$

${\displaystyle \underset{-}{\overset{1}{}}}\frac{1}{x^{\frac{1}{3}}}dx$

${\displaystyle \underset{4}{\overset{}{}}}\frac{1}{x^4}dx$

${\displaystyle \underset{3}{\overset{}{}}}{x}^{2}dx$