a. Rank the following functions by order of growth; that is, find an arrangement 81.82..... 830 of the functions satisfying 81 S2(82), 82 S2(83), 12(830). Partition your list into equivalence classes such that functions f(n) and g(n) are in the same class if and only if f(n) = (g(n)). 829 = Chapter 3 Growth of Functions Ig(Igen) 2le** (2) en n2 n! (lg n)! "/ign n 1g?n Ig(n!) 22" 1.2" milelen In 1 In Inn Igen 21 (Ign) en Ig* (Ign) 22215 en 4len (n + 1)! Ign nign n 21 22*+1 b. Give an example of a single nonnegative function f(n) such that for all func- tions gi(n) in part (a), f(n) is neither O(8:(n)) nor S2(g:(n))