University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 4 - Section 4.5 - Indeterminate Forms and L'Hôpital's Rule - Exercises - Page 248: 1



Work Step by Step

Since, $\lim\limits_{x \to -2}f(x)=\lim\limits_{x \to -2}\dfrac{x+2}{x^2-4}$ Check for indeterminate form: Thus, $f(-2)=\dfrac{-2+2}{4-4}=\dfrac{0}{0}$ Apply L-Hospital's rule: $\lim\limits_{a \to b}f(x)=\lim\limits_{a \to b}\dfrac{g'(x)}{h'(x)}$ Thus, $\lim\limits_{x \to -2}\dfrac{1}{2x}=\dfrac{1}{2(-2)}=\dfrac{-1}{4}$
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