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: 102


Check work for reasoning.

Work Step by Step

A removable discontinuity is a discontinuity that can be removed by simply "filling in" a point; it may be formed when the same factor cancels out from the numerator and the denominator. A non-removable discontinuity is one that cannot be removed by simply "filling" in a point; it may be caused by the denominator of a fraction equaling $0$ for a certain value of $x.$ a)$\dfrac{(x+2)}{(x+4)}$ has a non-removable discontinuity at $x=-4$ since the denominator is $0$ at that point. b)$\dfrac{(x+4)(x-4)}{(x-4)}$ has a removable discontinuity at $x=4$ since $(x-4)$ cancels out from both the numerator and the denominator. c)$\dfrac{(x+2)(x-4)}{(x+4)(x-4)}$ has both a removable discontinuity at $x=4$ and a non-removable discontinuity at $x=-4.$
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