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Big-O, Big-Theta and big-Omega notation can be extended to
Chapter 2, Problem 58E(choose chapter or problem)
Problem 58E
Big-O, Big-Theta and big-Omega notation can be extended to functions in more than one variable. For example, the statement f (x, y) is O (g(x, y)) means that there exist constants C, k1 , and k2 such that whenever x > k1 and y > k2 .
(Requires calculus) Show that if b > 1 and c and d are positive, then (logbn)c is O(nd), but nd is not O((logbn)c).
Questions & Answers
QUESTION:
Problem 58E
Big-O, Big-Theta and big-Omega notation can be extended to functions in more than one variable. For example, the statement f (x, y) is O (g(x, y)) means that there exist constants C, k1 , and k2 such that whenever x > k1 and y > k2 .
(Requires calculus) Show that if b > 1 and c and d are positive, then (logbn)c is O(nd), but nd is not O((logbn)c).
ANSWER:
Solution:
Step1
Given that
We have to show that if b > 1 and c and d are positive, then (logbn)c is O(nd), but nd is not O((logbn)c).