Solve the following recurrences asymptotically. For each recurrence show T(n) = (f(n)) for an appro- priate function f. Assume that T (n) is constant for sufficiently small n (i.e., there exist c, no 1 such that T(n) c for all n no). Justify your answers. You may use the master theorem (if applicable) or any of the other methods. a) T(n) = 6T(n/3) + n2 b) T (n) = 99 . T(n/ 100) + Vn c) T(n)=8T(n/2)-m3 d) T(n) 2T(n-1)+n e) T(n)=T(log n) + log log n. Hints: for parts (d), (e), you can guess the solution (say, by expanding the recursion tree) and then prove formally by induction. Another parenthesis: see Addendum of Lecture 3 for formal proofs of such statements