Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 1 - Functions and Limits - Review - True-False Quiz: 16

Answer

False.

Work Step by Step

One of the functions may not be defined at x=6, but the product might be. This gives us an idea to set up a counterexample: $f(x)=(x-6),$ $g(x)=\displaystyle \frac{1}{(x-6)}$ $\displaystyle \lim_{x\rightarrow 6}[f(x)g(x)]=\lim_{x\rightarrow 6}\frac{x-6}{x-6}=\lim_{x\rightarrow 6}1=1$ which does not equal $f(6)g(6)$ (g(6) is not defined). The problem statement is false.
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.