Calculate $y[n]$ analytically using convolution. Remember, $x[k]**h[k]=h[k]**x[k].$

$y[n]={\displaystyle \underset{k=-}{\overset{}{}}}x[k]h[n-k]={\displaystyle \underset{k=-}{\overset{}{}}}h[k]x[n-k]$

a$.,x[n]=(\frac{1}{2}{)}^{n}u[n],h[n]=[n-1]$

b$.x[n]=3^{n}u[-n],h[n]=[n+2]$

c$.,x[n]=[n-1]+[n+1],h[n]=(\frac{1}{3}{)}^{n}u[n)$

d$.x[n]=sin(2fn),h[n]=[n+5]$