Not as much for fun$-$ this one is in the scope of the class$4\mathrm{.}5-1$

Use the master method to give tight asymptotic bounds for the following recur$-$

rences.

a$.T(n)=2T(\frac{n}{4})+1.$

b$.T(n)=2T(\frac{n}{4})+\sqrt[\phantom{2}]{n}.$

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

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