Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 11 - Section 11.2 - Finding Limits Using Properties of Limits - Exercise Set - Page 1155: 77

Answer

The statement "I am working with functions $ f $ and $ g $ for which $\underset{x\to 4}{\mathop{\lim }}\,f\left( x \right)=0$, $\underset{x\to 4}{\mathop{\lim }}\,g\left( x \right)=0$, and $\underset{x\to 4}{\mathop{\lim }}\,\frac{g\left( x \right)}{f\left( x \right)}\ne 0$ " makes sense.

Work Step by Step

According to the quotient property of limits, $\underset{x\to a}{\mathop{\lim }}\,\frac{f\left( x \right)}{g\left( x \right)}=\frac{\underset{x\to a}{\mathop{\lim }}\,f\left( x \right)}{\underset{x\to a}{\mathop{\lim }}\,g\left( x \right)},\text{ }if\underset{x\to a}{\mathop{\lim }}\,g\left( x \right)\ne 0$ But here, $\underset{x\to 4}{\mathop{\lim }}\,f\left( x \right)=0$, $\underset{x\to 4}{\mathop{\lim }}\,g\left( x \right)=0$ So, the quotient property of limits cannot be applied. Thus, $\underset{x\to 4}{\mathop{\lim }}\,\frac{g\left( x \right)}{f\left( x \right)}\ne 0$ Thus, the given statement makes sense.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.