Problem $3$:

Determine the z$-$transforms and mention the ROC of the following signals.

$($a$)x_1(n)=\{\begin{array}{cc}(\frac{1}{3}{)}^n,& n0\\ (\frac{1}{2}{)}^{-n},& n<mn>0</mn>\end{array}$

$($b$)x_2(n)=\{\begin{array}{cc}(\frac{1}{3}{)}^n-2^n,& n0\\ 0,& n<mn>0</mn>\end{array}$

$($c$)x_3(n)=n(-1{)}^{n}u(n)$

$($d$)x_4(n)=n^{2}u(n)$