Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)

Published by Pearson
ISBN 10: 0-32193-104-1
ISBN 13: 978-0-32193-104-7

Chapter 13 - A Preview of Calculus: The Limit, Derivative, and Integral of a Function - Section 13.3 One-sided Limits; Continuous Functions - 13.3 Assess Your Understanding - Page 909: 41



Work Step by Step

Use the limit properties: (a) $\lim\limits_{x \to a} l(x)=l (a)$, where $a$ is a constant. We have: $\lim\limits_{x \to a} \dfrac{k(x)}{l(x)}=\dfrac{\lim\limits_{x \to a} k(x)}{\lim\limits_{x \to a} l(x)}$ $\lim\limits_{x\to -1^-}\dfrac{x^2-1}{x^3+1}=\lim\limits_{x\to -1^-}\dfrac{(x+1)(x-1)}{(x+1)(x^2-x+1)} \\=\dfrac{\lim\limits_{x\to -1^-} (x+1)(x-1)}{\lim\limits_{x\to -1^-}(x+1)(x^2-x+1)} \\=\dfrac{(-1)-1}{(-1)^2-(-1)+1} \\ =-\dfrac{2}{3}$
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