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: 37

Answer

$=\dfrac {2}{3}$

Work Step by Step

Factor each polynomial: $\lim _{x\rightarrow 1}\dfrac {x^{3}-x^{2}+x-1}{x^{4}-x^{3}+2x-2} \\=\lim _{x\rightarrow 1}\dfrac {x^{2}\left( x-1\right) +\left( x-1\right) }{x^{3}\left( x-1\right) +2\left( x-1\right) } \\=\lim _{x\rightarrow 1}\dfrac {\left( x-1\right) \left( x^{2}+1\right) }{\left( x-1\right) \left( x^{3}+2\right) }$ Cancel the common factors: $=\lim _{x\rightarrow 1}\dfrac {\left( x^{2}+1\right) }{\left( x^{3}+2\right) } \\=\dfrac {1+1}{1+2} \\=\dfrac {2}{3}$
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