   Chapter 2, Problem 12RQ ### 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

# Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement.If lim x → 0 f ( x ) = ∞   and   lim x → 0 g ( x ) = ∞ ,   then   lim x → 0 [ f ( x ) − g ( x ) ] = 0

To determine

Whether the statement, “if limx0f(x)= and limx0g(x)=, then limx0[f(x)g(x)]=0” is true or false.

Explanation

The given statement is false since the below example disproves the given statement.

Let f(x)=2x  and g(x)=1x.

Compute the limit of the functions as x approaches 0. That is, limx0(2x) and limx0(1x).

As x sufficiently close to 0 but x0, then the values of the functions f(x) and g(x) can be arbitrarily large.

Thus, the limit value of the functions does not exist. That is, limx0f(x)= and limx0g(x)=

### 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 