Rank the following functions by order of growth, that is find an arrangement 91, 92, ..., gn so that 91 = 2(92), 92 = (93), ..., gn-1 = (gn ), using asymptotic properties or by taking the limit. Each proof should be no more than 1-3 lines. Partition the set in equivalence classes, so that gi(n) and gj(n) are in the same equivalence class if and only if gi(n) = (gj (n)). n (2), n/2, (n/100) 1.5, n, n!, lgn, log10 n, lg(n!), 2log, n, 100n, lgn, en, 2n1, 2", nlgn, (n + 1)!, n ^, n In