3. [Asymptotics, 24 points] Sort the following 24 functions from asymptotically smallest to asymptotically largest, indicating ties if there are any. Do as much as you can, you will receive partial credit if you do not sort all of them. You will also need to turn in proofs that justify your answers to receive full credit! All logarithms are base 2 unless otherwise stated n'1.5-(n - 2)45 n1+(1/logn)log"(n/2) +2 og (log') log* 2" (log n)log'n log log(n!).J Tm 2log* n (1-10g HFi)" (1+20n)200n n(log n)2 1- lo n(log log n)/(logn) (log n)(n/2) (log n)logn n1/log logn log log n Tl log n lo TL To simplify notation, write f(n) g(n) to mean f(n) 0(g(n)), f(n) g(n) to mean f(n)-6(g(n)), and f(n) g(n) to mean f(n)-0(g(n)). For example, the functions n, n, (5), n3 could be sorted either as n3 (?) n> n or as n> n2 n