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: 20


$ f(x)=[x]$ has a jump discontinuity at $ x=n $.

Work Step by Step

The function $ f(x)=[x]$, has a jump discontinuity at $ x=n $ for every integer $ n $, since $$\lim _{x \rightarrow n+}[x]=n, \quad \lim _{x \rightarrow n-}[x]=n-1.$$ Moreover, $ f(x)=[x]$ is right-continuous, but not left continuous.
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