1. Let f(n) and g(n) be functions from positive integers to positive reals. We say f= O(g) (which means that "f grows no

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1 Let F N And G N Be Functions From Positive Integers To Positive Reals We Say F O G Which Means That F Grows No 1 (27.4 KiB) Viewed 32 times

1. Let f(n) and g(n) be functions from positive integers to positive reals. We say f= O(g) (which means that "f grows no faster than g") if there is a constant c> 0 such that f(n) ≤ exg(n). If g (n) grows no faster than f(n), we say f= Q(g). Iff=0(g) and f= Q(g), we say f= 8(g). Prove the relation of f(n) and g (n) for the following questions. (15) 2 Give Big-O notations of each formular. (6¹) (1) f(n)=n³ g(n)=100n² + 2000 (2) f(n)=50n² g(n)= n²+10 (3) f(n)=3n² +5 g(n) = 2n³