Give asymptotic upper bound for $T(n)$ in each of the following recurrence. Make your bounds as tight as possible.

$($a$)T(n)=9T(\frac{n}{2})+n^3$

$($b$)T(n)=7T(\frac{n}{2})+n^3$

$($c$)T(n)=\sqrt[\phantom{2}]{n}T(\sqrt[\phantom{2}]{n})+n$

$($d$)T(n)=2T(\frac{n}{2})+\frac{n}{logn}$

$($e$)T(n)=T(\frac{n}{3})+2T(\frac{n}{4})+n$