   Chapter 2, Problem 12RQ

Chapter
Section
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

In Exercises 5-8, graph the given function or equation. 2x3y=12

Finite Mathematics and Applied Calculus (MindTap Course List)

In Exercises 49-62, find the indicated limit, if it exists. 51. limx0x2xx

Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach

Solve each equation and check: 51x=7

Elementary Technical Mathematics 