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: 26

Answer

a) $21.$ b) $3.$ c) $3.$

Work Step by Step

a)By Theorem $1.3: $ $\lim\limits_{x\to c} p(x)=p(c)$ $\lim\limits_{x\to4}(2x^2-3x+1)=2(4)^2-3(4)+1=21.$ b)Using both Theorem $1.4: \lim\limits_{x\to c}\sqrt[n]{x}=\sqrt[n]{c}$ and Theorem $1.5: \lim\limits_{x\to c}(f(g(x)))=f(\lim\limits_{x\to c}g(x)):$ $\lim\limits_{x\to21}\sqrt[3]{x+6}=\sqrt[3]{\lim\limits_{x\to21}(x+6)}=\sqrt[3]{21+6}=3.$ c)By Theorem $1.5: \lim\limits_{x\to c}(g(f(x)))=g(\lim\limits_{x\to c}f(x)).$ $\lim\limits_{x\to4}g(f(x))=g(\lim\limits_{x\to4}f(x))=g(21)=3.$
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