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: 44



Work Step by Step

Factor each polynomial: $$\lim_{x\to -4^-}\frac{x^2+x-12}{x^2+4x}\\=\lim_{x\to -4^-}\frac{(x+4)(x-3)}{(x)(x+4)}.$$ Cancel the common factors: $$\lim_{x\to -4^-}\frac{(x-3)}{(x)}\\=\frac{-4-3}{-4}=\frac{7}{4}$$
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