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: 3

Answer

a) $\lim\limits_{x\to c^+}f(x)=0$ b) $\lim\limits_{x\to c^{-}}f(x)=0$ c) $\lim\limits_{x\to c}f(x)=0$ d) Continuous over the domain $(-\infty, 0)$and $(0, \infty)$ (in other words not continuous at $x=0.$)

Work Step by Step

a) As we approach c from the right, we get the limit to be equal to $0.$ b) As we approach c from the left, we get the limit to be equal to $0.$ c)The limit exists since $\lim\limits_{x\to c^+}f(x)=\lim\limits_{x\to c^{-}}f(x)$ d) The function is not continuous at $x=c$ since $f(c)\ne\lim\limits_{x\to c}f(x)$
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