(15 points) Big-O. For each function f (n) below, find (1) the smallest integer constant H such that f(n) O(nH), and (2) the largest positive real constant L such that f(n) 0(nL). Otherwise, indicate that H or L do not exist. All logarithms are with base 2. Your answer should consist of: (1) the correct value of H, (2) a proof that f(n) is O(nH), (3) the correct value of L, (4) a proof that f(n) is (n1). (a) fn)-n. (b) f(n) n(logn)3 (e) f(n) 2log n)