Rank Following Functions Order Growth Find Arrangement 81 82 817 Functions Satisfying 81 Q43900271
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) e (s(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 “log2 n”.) It may help to observe that if f(n) € 0(g(n)), then f(n) € (g(n)). (i) Vn (ii) nº (iii) 162 (iv) Ig((2n)!) (v) n (vi) n! (vii) 217 21-1 (viii) Ign fix) Ig(Ign) x) 2ign xi) (n+1)! xii) en xiii) 300n + 2.99793 x 108 xiv) (Ign)len xv) (3/2)” xvi) Igns xvii) n2″ Show transcribed image text 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) e (s(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 “log2 n”.) It may help to observe that if f(n) € 0(g(n)), then f(n) € (g(n)). (i) Vn (ii) nº (iii) 162 (iv) Ig((2n)!) (v) n (vi) n! (vii) 217 21-1 (viii) Ign fix) Ig(Ign) x) 2ign xi) (n+1)! xii) en xiii) 300n + 2.99793 x 108 xiv) (Ign)len xv) (3/2)” xvi) Igns xvii) n2″
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