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: 25


a) $3.$ b) $2.$ c) $2.$

Work Step by Step

a)By Theorem $1.3: $ $\lim\limits_{x\to c} p(x)=p(c)$ $\lim\limits_{x\to1}(4-x^2)=4-1^2=3.$ b)Using Theorem $1.4: \lim\limits_{x\to c}\sqrt[n]{x}=\sqrt[n]{c}.$ and Theorem $1.5: \lim\limits_{x\to c}(f(g(x)))=f(\lim\limits_{x\to c}g(x)).$ $\lim\limits_{x\to3}\sqrt{x+1}=\sqrt{\lim\limits_{x\to3}(x+1)}=\sqrt{3+1}=2.$ c)By Theorem $1.5: \lim\limits_{x\to c}(f(g(x)))=f(\lim\limits_{x\to c}g(x)).$ $\lim\limits_{x\to1}g(f(x))=g(\lim\limits_{x\to1}f(x))=g(3)=2.$
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