3. [12 points] Solve the following recurrences using the specified method (a) [6 points] T(n) = 8T(n/2) + n2. Use the master theorem. State which case and show that the conditions are satisfied. Theorem 4.1 (Master theorem) Let a 1 and b> 1 be constants, let f(n) be a function, and let T(n) be defined on the nonnegative integers by the recurrence T(n) = aT(n/b) + f(n) , or rn/b]. Then T(n) has the follow- where we interpret n/b to mean either ln/ ing asymptotic bounds: If f(n) 0(nlogba-r) for some constant > 0, then T(n) = (nlogba). If f(n)= (nlogb a), then T(n)= (nlogb a lg n). If f(n) = (nlogba+*) for some constant > 0, and if af(n/b) cf(n) for some constant c