Solve the following recurrences by giving tight ©-notation bounds in terms of n for sufficiently large n. Assume that T(.) represents the running time of an algorithm, i. e. T(n) is positive and non-decreasing function of n and for small constants c independent of n, T(C) is also a constant independent of n. Note that some of these recurrences might be a little challenging to think about at first. Each question has 4 points. For each question, you need to explain how the Master Theorem is applied and state your answer . (a) T(n) = 4T(n/2) + n^2log n.
(b) T(n) = 8T(n/6) + n log n.
(c) T(n) = √6006T (n/2) + n √6006
(d) T(n) = 10T(n/2) + 2n.
(e) T(n) = 2T(√n) + log2n. .