Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 2 - Review - True-False Quiz: 7

Answer

The statement is false.

Work Step by Step

This statement is false. Here's an example to disprove: $\lim\limits_{x\to5}f(x)=\lim\limits_{x\to5}(x^2-5x)=5^2-5\times5=0$ $\lim\limits_{x\to5}g(x)=\lim\limits_{x\to5}(x-5)=5-5=0$ However, $$\lim\limits_{x\to5}\frac{x^2-5x}{x-5}$$$$=\lim\limits_{x\to5}\frac{x(x-5)}{x-5}$$$$=\lim\limits_{x\to5}x$$$$=5$$ That means $\lim\limits_{x\to5}\frac{x^2-5x}{x-5}$ does exist.
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