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# Solved: Big-O, Big-Theta and Big-Omega notation can be ISBN: 9780073383095 37

## Solution for problem 57E Chapter 3.2

Discrete Mathematics and Its Applications | 7th Edition

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Problem 57E

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 constant C, k1 and k2 such that whenever x > k1 and y > k2 .(Requires calculus) Show that if c > d > 0. then nd is O(nc), but nc is not O(nd).

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Solution:Step1Given thatWe have to show that if c > d > 0. then is O(), but is not O().Step2 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 . Let us assume that f and g is functions from the set of integers.We can say that f(x) is O(g(x)) if there are constants C and k such that Where >k.The constants C and k are said to be witnesses to the relationship.If c > d > 0 (d

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##### ISBN: 9780073383095

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Solved: Big-O, Big-Theta and Big-Omega notation can be