Using -notation, provide asymptotically tight bounds in terms of n for the solution to each of the following recurrences. Assume each recurrence has a non-trivial base case of T(n) = (1) for all n n0 where n0 is a suitably large constant. For example, if asked to solve T(n) = 2T(n/2) + n, then your answer should be (n log n). Give a brief explanation for each solution. [Hint: use recursion trees.]

1) T(n) = 2T(n/2) + n lg^2 n