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: 33



Work Step by Step

Factor each polynomial: $\lim _{x\rightarrow 1}\dfrac {x^{3}-1}{x-1} \\=\lim _{x\rightarrow 1}\dfrac {\left( x-1\right) \left( x^{2}+x+1\right) }{x-1}$ Cancel the common factors: $\\=\lim _{x\rightarrow 1}\left( x^{2}+x+1\right) \\=1^{2}+1+1 \\=3$
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