Select 10 formulas from the above problem to do the comparisons using big O, big \theta, and big \omega . (Rank them. You can just indicate which one is big, which one is the second, etc. using these notations.)

Please write neatly and explain the steps on paper. Thanks in advance.

a. Rank the following functions by order of growth; that is, find an arrangement g1, 92, ..., 930 of the functions satisfying g = 22(g), g2 = 12(93), ..., 929 = 12(930). Partition your list into equivalence classes such that f(n) and g(n) are in the same class if and only if f(n) = (g(n)). lgold n) 2lg* (2)lgn n2 n! (Ign)! n3 lgn ngon!) 22" n/lgn In Inn n. 2" ng Ign Inn 1 e" 21gn (Ig nylon Ig* (Ign) 221gn (n + 1)! Vign nign 2 220+1