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 - 1.4 Exercises: 5

Answer

a) $\lim\limits_{x\to c^+}f(x)=-3$ b) $\lim\limits_{x\to c^{-}}f(x)=3$ c) $\lim\limits_{x\to c}f(x)$ doesnt exist The function is not continuous at $x=c=2.$

Work Step by Step

a) As we approach c from the right, we get the limit to be equal to $-3.$ b) As we approach c from the left, we get the limit to be equal to $3.$ c)The limit does not exist since $\lim\limits_{x\to c^+}f(x)\ne\lim\limits_{x\to c^{-}}f(x).$ d) The function is not continuous at $x=c$ since $\lim\limits_{x\to c}f(x)$ does not exist.
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