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: 34

Answer

$4$

Work Step by Step

Factor each polynomial: $\lim _{x\rightarrow 1}\dfrac {x^{4}-1}{x-1} \\=\lim _{x\rightarrow 1}\dfrac {x^{4}-1^{4}}{x-1} \\=\lim _{x\rightarrow 1}\dfrac {\left( x^{2}-1^{2}\right) \left( x^{2}+1^{2}\right) }{x-1} \\=\lim _{x\rightarrow 1}\dfrac {\left( x-1\right) \left( x+1\right) \left( x^{2}+1^{2}\right) }{x-1}$ Cancel the common factors: $\\=\lim _{x\rightarrow 1}\left( x+1\right) \left( x^{2}+1\right) \\=\left( 1+1\right) \left( 1+1\right) \\=2(2) \\=4$
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