Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 2 - Limits - 2.4 Limits and Continuity - Exercises - Page 67: 34


Infinite discontinuity

Work Step by Step

We are given the function: $f(x)=\ln |x-4|$ Compute the left hand and right hand limits: $\displaystyle\lim_{x\rightarrow 0^{-}} \ln |x-4|=\infty$ $\displaystyle\lim_{x\rightarrow 0^{+}} \ln |x-4|=\infty$ Therefore we got: $\displaystyle\lim_{x\rightarrow 0^{-}} \ln |x-4|=\displaystyle\lim_{x\rightarrow 0^{+}} \ln |x-4|=\infty$ As the function is not defined in $x=4$ and both its one-sided limits are infinite, the function has an infinite discontinuity.
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