$(60$ points$)$ Assume that $T(1)in(1).$ Solve the following recurrences using the recursion tree

method.

a$.T(n)=4T(\frac{n}{2})+n^2$

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

c$.T(n)=T(n-2)+n$

d$.T(n)=4T(\frac{n}{2})+n$

e$.T(n)=2T(n-2)+1$

f$.T(n)=T(\frac{n}{2})+T(\frac{n}{3})+n$