Use the master theorem to find tight asymptotic bounds for the following re-currences. Justify your answers (by showing which case of the master theorem applies, and why.) Assume that T(1) =1. 16T(n/4) +n^2 T(n) = (n/4) + sqrt n Consider the following recursive function for n >= 0: Set up a runtime recurrence for the runtime T(n) of this algorithrm. Solve tins runtime recurrence using the master theorem. Use strong induction to prove that T(n) element 0(log n) where T(1) = d_0 and T(n) = T(n/ 2) + d_n (for n >= 2)