Single Variable Calculus: Concepts and Contexts, Enhanced Edition
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
4th Edition
ISBN: 9781337687805
Author: James Stewart
Publisher: Cengage Learning
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Chapter D, Problem 24E
To determine

To prove:

  limnn3= by using definition 4 .

Expert Solution & Answer
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Answer to Problem 24E

it is proved that limnn3= so.

Explanation of Solution

Given information:

  limnn3=

Proof:

Let’s assume notation as a=n3

There is need to prove that limnn3=

By definition 4 ,

The notation limnn3= means that for every positive number M there is an integer such that.

In case n>N then an>M .

Suppose that M be an positive integer such that

  n3>Mn>M3n3>Man<M

Thus, from the definition 4 result is limnn3= .

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Limits and Continuity; Author: The Organic Chemistry Tutor;https://www.youtube.com/watch?v=9brk313DjV8;License: Standard YouTube License, CC-BY