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[3] Rank the following functions by order of growth; that is, find an arrangement 81, 82, ..., 817 of the functions below satisfying 81 O(82), 82 0(83), 89 0(817) 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)). Robust mathematical proofs are preferred, but some credit might be obtained for correct answers obtained through "hand waving arguments (the wilder the waving, the lower the grade). (And note that "Ign" is "logzn".) It may help to observe that if f(n) 0(g(n)), then f(n) 8((n)). (i) Vn (iii) 1613 (iv) Ig((2n)!) (vi) n! (vii) 2152-1 (viii) Ign (ix) Ig(Ign) (x) 21gn (xi) n+1)! (xii) valen (xiii) 300n + 2.99793 x 108 (xiv) (Ign)len (xv) (3/2)" (xvi) igns (xvii) n2