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 73: 55


$c=-1$ and $c=6$

Work Step by Step

$$\lim _{x \rightarrow c} \frac{x^{2}-5 x-6}{x-c}$$ This limit will exist, provided that $x-c$ is a factor of the numerator. (Otherwise there will be an infinite discontinuity at $x=c$.) Since $$x^{2}-5 x-6=(x+1)(x-6),$$ then we know that this occurs for $c=-1$ and $c=6$.
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