Problem 1. This question reviews asymptotic notation. You may assume the following inequalities for this question (and throughout the course): For any constant c> 1, (logn) = o(n), n = o(ne+1) c" = 0((c+1)"), (n/2)(n/2) - (n!), n! = n(n). (a) Rank the following functions based on their asymptotic value in the increasing order, i.e., list them as functions f1. 12. f3,..., fo such that fi = O(f2), f2 = ($3),..., fs = O(f9). Remember to write down your proof for each equation fi= (fi+1) in the sequence above. (15 points) nlogn log n 21 100n n! n gn 3984 logan n Hint: For some of the proofs, you can simply show that fi(n)