Use the master method to give tight asymptotic bounds for the following recurrences.

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

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

c$)T(n)=T(4\frac{n}{5})+n$

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

e$)T(n)=3T(\frac{n}{9})+\sqrt[\phantom{2}]{n}$