Question $2-$ Recurrence Relations $[20\%]$

For each of the following recurrence relations, solve the recurrence and state the $$ bound.

$($a$)T(n)=T(n-1)+3$;$T(0)=0.$

$($b$)T(n)=3T(\frac{n}{3})+n$;$T(1)=0,$ you may assume that $n$ is a power of $3.$

$($c$)T(n)=4T(\frac{n}{3})+1$;$T(1)=0,$ you may assume that $n$ is a power of $3.$

$($d$)T(n)=nT(\frac{n}{2})+n-1$;$T(1)=1,$ you may assume that $n$ is a power of $2.$