Question: For each function i below, give the simplest function G. such that lie (9) and then order the functions asymptotically, i.e., produce an order f1.

For each function i below, give the simplest function G. such

For each function i below, give the simplest function G. such that lie (9) and then order the functions asymptotically, i.e., produce an order f1. 12. ... such that fie (i+1). If two functions were in the same (g), then group them together in the order. Think about how you might apply the properties in the previous problem here. (a) Sa(n) = 22n-1 (b) f(n) = log2 (5n) logg(4n2) (c) Sa(n) = 100100 (d) fe(n) = n log2 (4") (e) /.(n) = 20.5 +0.4 (1) f(n) = log2 (5n x 4n2) (E) /, (n) = 5n logio(n-4) (h) sh(n) = 21-24 (i) f(n) = 2log (n) + V3n 6) Si(n) = 45 (k) fx(n) = 212+1 (1) fe(n) = Vn" + 3n+1 (m) fm(n) = (i+1) (n) [n(n) = 2m log2 (n) (0) fe(n) = 4logy (P) Sp(n) = 12.2m (q) q(n) = log2 (n!) (T) fr(n) = D. (3) (s) f(n) = 0 (t) f(n) = (log, n) logan For each function i below, give the simplest function G. such that lie (9) and then order the functions asymptotically, i.e., produce an order f1. 12. ... such that fie (i+1). If two functions were in the same (g), then group them together in the order. Think about how you might apply the properties in the previous problem here. (a) Sa(n) = 22n-1 (b) f(n) = log2 (5n) logg(4n2) (c) Sa(n) = 100100 (d) fe(n) = n log2 (4") (e) /.(n) = 20.5 +0.4 (1) f(n) = log2 (5n x 4n2) (E) /, (n) = 5n logio(n-4) (h) sh(n) = 21-24 (i) f(n) = 2log (n) + V3n 6) Si(n) = 45 (k) fx(n) = 212+1 (1) fe(n) = Vn" + 3n+1 (m) fm(n) = (i+1) (n) [n(n) = 2m log2 (n) (0) fe(n) = 4logy (P) Sp(n) = 12.2m (q) q(n) = log2 (n!) (T) fr(n) = D. (3) (s) f(n) = 0 (t) f(n) = (log, n) logan

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