Give asymptotic bounds for $T(n)$ in each of the following recurrences. Assume that $T(n)$ is

constant for $n2.$ Make your bounds as tight as possible, and justify your answers.

$($a$)T(n)=8T(\frac{n}{2})+n^3\sqrt[\phantom{2}]{n}$

$($b$)T(n)=T(n-1)+logn$

$($c$)T(n)=3T(\frac{n}{27})+n^{0\mathrm{.}25}$

$($d$)T(n)=16T(\frac{n}{4})+n^{2}lo{g}^{2}n$