(10 pts) Use O, N, or O to relate each of the following pairs of functions. In particular, you need to write your answer as f(n) E O(g(n)), f(n) E (g(n)), or f(n) E O(g(n)). In case f (n) E O(g(n)), you will not receive credit if you write f(n) E O(g(n)) or f(n) E N(g(n)), although both are implied by f(n) E O(g(n)). (a) g(n) = 100 (log n), f(n) = 2 x i. i=1 (b) g(n) = 1.0001", f(n) = n 3000 (c) g(n) = E(3i), f(n) = 3 x n +i. i=1 i=1 (d) g(n) = 2 x n!, f(n) = (2 n)!. 200 (e) g(n) = n.001, f (n) = E i=1