Use the method of recursion trees to solve the following recurrences:

$($a$)A(n)=2A(\frac{n}{3})+O(n^{\frac{1}{2}}).$

$($b$)B(n)=3B(\frac{n}{2})+O(n^3).$

For each recursion tree, draw three layers $($root$,$ children, grandchildren$)$ of the recursion

tree. $($You may upload a photo of your trees for this problem, or just describe the trees,

e$.$g$.$ "there are four children, each with label $\frac{n^3}{9},")$