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 - 14.2 Algebra Techniques for Finding Limits - 14.2 Assess Your Understanding - Page 884: 47



Work Step by Step

General formula for average rate of change from $a$ to $b$: $\frac{f(b)-f(a)}{b-a}.$ Factor each polynomial: $$\lim_{x\to -1}\frac{f(x)-f(-1)}{x-(-1)}\\=\lim_{x\to -1}\frac{x^2+2x-((-1)^2+2(-1))}{x+1}\\=\lim_{x\to -1}\frac{x^2+2x+1}{x+1}\\=\lim_{x\to -1}\frac{(x+1)(x+1)}{(x+1)}.$$ Cancel the common factors: $$\lim_{x\to -1}(x+1)\\=(-1)+1=0$$
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