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: 7

Answer

False

Work Step by Step

"Difference Law: The limit of a difference is the difference of the limits" $\lim\limits_{x\to a}[f(x)-g(x)] = \lim\limits_{x \to a}f(x) -\lim\limits_{x \to a}g(x)$ If the individual limits of each function exist. You cannot subtract a limit which does not exist. Thus the statement: $\lim\limits_{x \to 4}[\frac{2x}{x-4}-\frac{8}{x-4}] = \lim\limits_{x \to 4}\frac{2x}{x-4} - \lim\limits_{x \to 4}\frac{8}{x-4}$ Is not true because the individual limits diverge (do not exist)
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