# Solved: Big-O, big-Theta, And big-Omega notation can be ## Problem 55E Chapter 3.2

Discrete Mathematics and Its Applications | 7th Edition

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Problem 55E

Big-O, big-Theta, And big-Omega notation can be extended to functions in more than one variable. For example, the statement is means that the exist constants C, k1 , and k2 such that whenever and . Show that is O(xy).

Step-by-Step Solution:
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Step-1:

In this problem we need to show that Note:

Let us consider f and g are functions from the set of integers to the set of real numbers.

The estimate value can be said that f(x) is O(g(x)) if there are constants C and k such that , where  C > 0 and  x> k.The constants C and k are called the witnesses to the relationship.

The definition of f(x) is O(g(x)) says that f(x) grows slower than some fixed multiple of g(x) as x grows without bound.

Step-2:

Consider , We...

Step 2 of 3

Step 3 of 3

##### ISBN: 9780073383095

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Solved: Big-O, big-Theta, And big-Omega notation can be

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