Calculus 10th Edition

Published by Brooks Cole
ISBN 10: 1-28505-709-0
ISBN 13: 978-1-28505-709-5

Chapter 1 - Limits and Their Properties - Review Exercises: 14

Answer

$\lim\limits_{x\to-5}\sqrt[3]{x-3}=\sqrt[3]{-8}=-2.$

Work Step by Step

Using both Theorem $1.4: \lim\limits_{x\to c}\sqrt[n]{x}=\sqrt[n]{c}$ and Theorem $1.5: \lim\limits_{x\to c}(f(g(x)))=f(\lim\limits_{x\to c}g(x)).$ $\lim\limits_{x\to-5}\sqrt[3]{x-3}=\sqrt[3]{\lim\limits_{x\to-5}(x-3)}=\sqrt[3]{-5-3}=\sqrt[3]{-8}=-2.$
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