Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 7: Transcendental Functions - Section 7.5 - Indeterminate Forms and L'Hopital's Rule - Exercises 7.5 - Page 409: 1

Answer

$\dfrac{-1}{4}$

Work Step by Step

Consider: $\lim\limits_{x \to -2}f(x)=\lim\limits_{x \to -2}\dfrac{x+2}{x^2-4}$ Need to check that the limit has an indeterminate form. Thus, $f(-2)=\dfrac{-2+2}{4-4}=\dfrac{0}{0}$ Now, apply L-Hospital's rule such as: $\lim\limits_{a \to b}f(x)=\lim\limits_{a \to b}\dfrac{g'(x)}{h'(x)}$ This implies: $\lim\limits_{x \to -2}\dfrac{1}{2x}=\dfrac{1}{2(-2)}=\dfrac{-1}{4}$
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