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(Requires calculus) Show that if d is positive and b > I,

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

Solution for problem 59E 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 59E

(Requires calculus) Show that if d is positive and b > I, then nd is O(bn) but bn is not O(nd).

Step-by-Step Solution:

Step 1</p>

In this problem we have to show that if d is a positive and b > 1, then  but .

Step 2</p>

Function  is called  if there exist constant c and k such that

 where

We have , and d is positive

So, ,

We get indeterminate form.

So, using L’ hospital’s  rule

  

Using again and again we get,

 

Or,

Or,

For

We can express

Therefore .

Step 3 of 3

Chapter 3.2, Problem 59E is Solved
Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. The answer to “(Requires calculus) Show that if d is positive and b > I, then nd is O(bn) but bn is not O(nd).” is broken down into a number of easy to follow steps, and 21 words. Since the solution to 59E from 3.2 chapter was answered, more than 291 students have viewed the full step-by-step answer. The full step-by-step solution to problem: 59E from chapter: 3.2 was answered by , our top Math solution expert on 06/21/17, 07:45AM. This full solution covers the following key subjects: Calculus, Positive, requires, show. This expansive textbook survival guide covers 101 chapters, and 4221 solutions.

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