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Show that 8x3 + 12x + 100 logx is O(x3).

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

Solution for problem 16E Chapter 3.SE

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 16E

Show that 8x3 + 12x + 100 logx is O(x3).

Step-by-Step Solution:

Step 1</p>

For two given functions  and , we can say that  is  if and only if there exists two constants B and l , such that  whenever  .

In this problem we are asked to show that is .

Step 2</p>

For two given functions and , if is and is , then the sum of the two functions is .  

First we will estimate .

We can write that for

             

Multiplying both sides by x, we get

Since  we can write

         

Adding  both sides, we get

 which is same as .

Since  for , we can write that

for

Therefore with witnesses and , is .

To estimate , we do as follows

We know that , hence we write

 for

Since  for , we can write that

 for

Therefore with witnesses and ,is .

Step 3 of 3

Chapter 3.SE, Problem 16E is Solved
Textbook: Discrete Mathematics and Its Applications
Edition: 7
Author: Kenneth Rosen
ISBN: 9780073383095

The full step-by-step solution to problem: 16E from chapter: 3.SE was answered by , our top Math solution expert on 06/21/17, 07:45AM. Since the solution to 16E from 3.SE chapter was answered, more than 251 students have viewed the full step-by-step answer. The answer to “Show that 8x3 + 12x + 100 logx is O(x3).” is broken down into a number of easy to follow steps, and 10 words. This textbook survival guide was created for the textbook: Discrete Mathematics and Its Applications, edition: 7. Discrete Mathematics and Its Applications was written by and is associated to the ISBN: 9780073383095. This full solution covers the following key subjects: logx, show. This expansive textbook survival guide covers 101 chapters, and 4221 solutions.

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