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 - 1.3 Exercises: 14

Answer

$\lim\limits_{x\to2}\sqrt[3]{12x+3}=3.$

Work Step by Step

By Theorem $1.4: \lim\limits_{x\to c}\sqrt[n]{x}=\sqrt[n]{c}.$ By Theorem $1.5: \lim\limits_{x\to c}(f(g(x)))=f(\lim\limits_{x\to c}g(x)).$ $\lim\limits_{x\to2}\sqrt[3]{12x+3}=\sqrt[3]{\lim\limits_{x\to2}(12x+3)}=\sqrt[3]{12(2)+3}=3.$
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