Precalculus (10th Edition)

Published by Pearson
ISBN 10: 0-32197-907-9
ISBN 13: 978-0-32197-907-0

Chapter 14 - A Preview of Calculus: The Limit, Derivative, and Integral of a Function - 14.3 One-sided Limits; Continuous Functions - 14.3 Assess Your Understanding - Page 890: 43

Answer

$\frac{3}{2}$

Work Step by Step

Factor each polynomial: $$\lim_{x\to -2^+}\frac{x^2+x-2}{x^2+2x}\\=\lim_{x\to -2^+}\frac{(x+2)(x-1)}{(x)(x+2)}.$$ Cancel the common factors: $$\lim_{x\to -2^+}\frac{(x-1)}{(x)}\\=\frac{-2-1}{-2}=\frac{3}{2}$$
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