Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 2 - Limits - 2.5 Evaluating Limits Algebraically - Exercises - Page 72: 6


$$\lim _{x \rightarrow 8} \frac{x^2-64}{x-9 }=0$$

Work Step by Step

Given $$\lim _{x \rightarrow 8} \frac{x^2-64}{x-9}$$ let $$ f(x) = \frac{x^2-64}{x-9}$$ Since, we have $$ f(8)=\frac{64-64}{8-9}=\frac{0}{-1}=0$$ So, we get \begin{aligned} L&=\lim _{x \rightarrow 9} \frac{x^2-64}{x-9}\\ &= \frac{64-64}{8-9}\\ &= \frac{0}{-1}\\ &=0 \end{aligned}
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