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Show that x3 is O(x4) but that x4 is not O(x3).

Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen ISBN: 9780073383095 37

Solution for problem 10E Chapter 3.2

Discrete Mathematics and Its Applications | 7th Edition

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Discrete Mathematics and Its Applications | 7th Edition | ISBN: 9780073383095 | Authors: Kenneth Rosen

Discrete Mathematics and Its Applications | 7th Edition

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Problem 10E

Show that x3 is O(x4) but that x4 is not O(x3).

Step-by-Step Solution:

SolutionStep 1Let us assume that x > 1 then >So, the first term that is will influence.Then, instead of we can write as .Because will grow as slow as Hence, Where n = 4, C = 1 and k = 1So the growth of the function is O().Hence, it is proved that has the growth of function O().

Step 2 of 3

Chapter 3.2, Problem 10E is Solved
Step 3 of 3

Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

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Show that x3 is O(x4) but that x4 is not O(x3).