Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 1 - Limits and Their Properties - 1.3 Exercises - Page 67: 43


$\lim\limits_{x \to -1}\dfrac{x^{2}-1}{x+1}=-2$

Work Step by Step

$\lim\limits_{x \to -1}\dfrac{x^{2}-1}{x+1}$ Factor the numerator and simplify: $\lim\limits_{x \to -1}\dfrac{x^{2}-1}{x+1}=\lim\limits_{x \to -1}\dfrac{(x-1)(x+1)}{x+1}=\lim\limits_{x \to -1}x-1$ Apply direct substitution to evaluate the limit: $\lim\limits_{x \to -1}x-1=-1-1=-2$
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