Calculus: Early Transcendentals (2nd Edition)

Published by Pearson
ISBN 10: 0321947347
ISBN 13: 978-0-32194-734-5

Chapter 2 - Limits - 2.3 Techniques for Computing Limits - 2.3 Exercises: 75

Answer

$\frac{1}{3}$

Work Step by Step

$\lim\limits_{x \to 1}$ $\frac{\sqrt[3] x-1}{x-1}$ = $\lim\limits_{x \to 1}$ $\frac{\sqrt[3] x-1}{(\sqrt[3] x-1)(\sqrt[3] x^{2}+\sqrt[3] x+1)}$ = $\lim\limits_{x \to 1}$ $\frac{1}{(\sqrt[3] x^{2}+\sqrt[3] x+1)}$ = $\frac{1}{(\sqrt[3] 1^{2}+\sqrt[3] 1+1)}$ = $\frac{1}{(1+1+1)}$ =$\frac{1}{3}$
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