   Chapter 2.4, Problem 27E ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343

#### Solutions

Chapter
Section ### Single Variable Calculus: Early Tr...

8th Edition
James Stewart
ISBN: 9781305270343
Textbook Problem

# Prove the statement using the ε, δ definition of a limit. lim x → 0 | x | = 0

To determine

To prove: The limit of a function limx0(|x|) is equal to 0 by using the ε,δ definition of a limit.

Explanation

Definition used:

“Let f be a function defined on some open interval that contains the number a, except possibly at a itself. Then, the limit of f(x) as x approaches a is L, limxaf(x)=L if for every number ε>0 there is a number δ>0 such that if 0<|xa|<δ then |f(x)L|<ε”.

To guess: The number δ.

Let ε be a given positive integer. Here, f(x)=|x|, a=0 and L=0.

By the definition of ε and δ, it is enough to find a number δ such that if 0<|x0|<δ then ||x|0|<ε.

Consider ||x|0|

### Still sussing out bartleby?

Check out a sample textbook solution.

See a sample solution

#### The Solution to Your Study Problems

Bartleby provides explanations to thousands of textbook problems written by our experts, many with advanced degrees!

Get Started

#### In problems 5-8, write the following sets in a second way. 5.

Mathematical Applications for the Management, Life, and Social Sciences

#### If f(x) = 2e3x, f(x) = a) 2e3x b) 2xe3x c) 6e3x d) 6xe3x

Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th

#### Self Check Factor:4a28ab .

College Algebra (MindTap Course List) 