Calculus (3rd Edition)

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

Chapter 7 - Exponential Functions - 7.7 L'Hôpital's Rule - Exercises - Page 366: 2



Work Step by Step

Since we have $$ \lim _{x \rightarrow -5} \frac{ x^{2}-25 }{5-4x-x^2}= \frac{0}{0}. $$ Then we can apply L’Hôpital’s Rule as follows $$ \lim _{x \rightarrow -5} \frac{ x^{2}-25 }{5-4x-x^2}= \lim _{x \rightarrow -5} \frac{ 2x }{ -4-2x}=\frac{-10}{6}=-\frac{5}{3}. $$
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