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 - Concept and Vocabulary Check - Page 1153: 9


The complete statement is “$\underset{x\to a}{\mathop{\lim }}\,\text{ }\frac{f\left( x \right)}{g\left( x \right)}=$$\frac{L}{M}$$ M\ne 0$.

Work Step by Step

The limit of the quotient of two functions equals the quotient of their limits. Also, the limit of the denominator is not zero. That is: The limit of a quotient: If $\underset{x\to a}{\mathop{\lim }}\,\text{ }f\left( x \right)=L\text{ and }\underset{x\to a}{\mathop{\lim }}\,\text{ }g\left( x \right)=M\text{ };M\ne 0$, then $\underset{x\to a}{\mathop{\lim }}\,\text{ }\frac{f\left( x \right)}{g\left( x \right)}=\frac{\underset{x\to a}{\mathop{\lim }}\,f\left( x \right)}{\underset{x\to a}{\mathop{\lim }}\,g\left( x \right)}=\frac{L}{M}\text{ };M\ne 0$ Before applying the quotient property, find the limit of the denominator. If this limit is not zero, apply the quotient property. And if the limit of the denominator is zero, the quotient property cannot be used. For example: Let $ f\left( x \right)=x $ and $ g\left( x \right)=2$, $\begin{align} & \underset{x\to 7}{\mathop{\lim }}\,\frac{f\left( x \right)}{g\left( x \right)}=\frac{\underset{x\to 7}{\mathop{\lim }}\,f\left( x \right)}{\underset{x\to 7}{\mathop{\lim }}\,g\left( x \right)} \\ & =\frac{\underset{x\to 7}{\mathop{\lim }}\,x}{\underset{x\to 7}{\mathop{\lim }}\,2} \\ & =\frac{7}{2} \end{align}$ Therefore, the complete fill for the blank in the statement “$\underset{x\to a}{\mathop{\lim }}\,\text{ }\frac{f\left( x \right)}{g\left( x \right)}=\frac{L}{M}$,$ M\ne 0$”.
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.