Here o is "little-o" and not "big-o".

Note 1: We defined asymptotic notation for functions f:N + N, but the same definitions work for real-valued functions f:N + R. All functions in question 1 are real-valued. Note 2: In denotes the natural logarithm. 1. (a) (5 pts) Find f(n), g(n) > 1 such that in f(n) = o(ln g(n)) and f(n) + 0(g(n)). (b) (5 pts) Prove that for f(n), g(n) > 1 if In f(n) = o(ln g(n)) and g(n) oo then f(n) = 0(g(n)). (c) (5 pts) Let f(n), g(n) > 1 and suppose that f(n) = N(g(n)). Does it follow that in f(n) S2(in g(n))? If yes, give a proof; if not, give a counterexample. =