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: 28

Answer

$-1$

Work Step by Step

Recall: (1) $\lim _{x\rightarrow c}\left( f\left( x\right) \right) ^{n}=\left( \lim _{x\rightarrow c}f\left( x\right) \right) ^{n}$ (2) $\lim _{x\rightarrow c}f(x) = f(c)$ Use the rules above to have: $ \lim _{x\rightarrow -1}\left( 2x+1\right) ^{\frac {5}{3}} \\=\left( \lim _{x\rightarrow -1}\left( 2x+1\right) \right) ^{\frac {5}{3}} \\=\left(2(-1)+1\right)^{5/3} \\=\left( -2+1\right) ^{\frac {5}{3}} \\=-1^{\frac {5}{3}} \\=-1$
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