1. (20 pts) For each of the following pairs of functions, indicate whether it is one of the three cases: f(n)=O(g(n)),f(n)=(g(n)), or f(n)=(g(n)). For each pair, you need to give both the answer and the proof. (1) f(n)=5n and g(n)=n32n (2) f(n)=nlogn and g(n)=nlognn 2. (24 pts) Order the following list of functions in increasing order asymptotically (i.e., from small to large, as we did in class) (loglogn)!,log(logn)2,231000,1000,3log3n,n(logn)1000,nlogn,n2loglogn, log(n100),(logn)2,2n,23n