2. (15 points) Big-O. For each function f(n) below, find (1) the smallest integer constant H such that f(n) = O(n), and (2) the largest positive real constant L such that f(n) = N(n). Otherwise, state that H or L do not exist. All logarithms have 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 (nl). (a) f(n) = nlogin log(log n) (b) f(n) = 2X=1 Vk: Vn k (c) f(n) = _, k: 2-k (d) f(n) = 2X=1 k log k (e) f(n) = EK=1 TTLE 2. (15 points) Big-O. For each function f(n) below, find (1) the smallest integer constant H such that f(n) = O(n), and (2) the largest positive real constant L such that f(n) = N(n). Otherwise, state that H or L do not exist. All logarithms have 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 (nl). (a) f(n) = nlogin log(log n) (b) f(n) = 2X=1 Vk: Vn k (c) f(n) = _, k: 2-k (d) f(n) = 2X=1 k log k (e) f(n) = EK=1 TTLE