Give a asymptotic solutions using Big theta notation for eac

Give a asymptotic solutions (using Big theta notation) for each of the following recurrence equations.
T(n) = 6T(n/3) + n^2

Solution

T(n) = 6T(n/3) + n*n

Using Master method:

if T(n) = aT(n/b) + h(n)

Here a=6 b=3 h(n)=n*n

Thus h(n) is O(n^log_ba-E)

So, O(n^log₃6-E) for any E<=1

Thus O(n^log₃6).