Need this Solve the following recurrence using Master Theore

Need this:

Solve the following recurrence using Master Theorem. State the case and the constant values used: T(n) = 11 T(n/3) + 8n^3 Upload a file with your solution.

Solution

IN Master\'s theorem we have general form of equation as foolows

T(n)= aT(n/b)+g(n)

Here a=11 b =3 and g(n)=8n³

Now we calculate f(n)= n^log_ba

Which gives us n ^log₃11

Now we compare f(n) and g(n)

If f(n) < g(n) then T(n) =O(g(n))

else if f(n)=g(n) T(n)= O(T(n)log n)

else T(n) = O(f(n))

Here in this question log₃11 is less than 3 therefore f(n) <g(n)

Therefore T(n)= O(n³)