21. Let f(n) = n² + 20 and g(n) = n³. (a) Show that f(n) is O(g(n)) by finding a positive integer A for which f(n) < A g(n) for all n ≥ 1. (b) Show that f(n) is O(g(n)) by finding a positive integer N for which f(n) < g(n) for all n > N. (c) Use proof by contradiction to show that g(n) is not O(f(n)).
21. Let f(n) = n² + 20 and g(n) = n³. (a) Show that f(n) is O(g(n)) by finding a positive integer A for which f(n) < A g(n) for all n ≥ 1. (b) Show that f(n) is O(g(n)) by finding a positive integer N for which f(n) < g(n) for all n > N. (c) Use proof by contradiction to show that g(n) is not O(f(n)).
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.1: Infinite Sequences And Summation Notation
Problem 65E
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