## Calculus (3rd Edition)

Published by W. H. Freeman

# Chapter 2 - Limits - 2.4 Limits and Continuity - Exercises - Page 67: 21

#### Answer

$f(x)=[\frac{1}{2}x]$, has a jump discontinuity at $x=2n$ for every integer $n$,

#### Work Step by Step

The function $f(x)=[\frac{1}{2}x]$, has a jump discontinuity at $x=2n$ for every integer $n$, since $$\lim _{x \rightarrow 2n+}[x]=n, \quad \lim _{x \rightarrow 2n-}[x]=n-1.$$ Moreover, $f(x)=[x]$ is right-continuous because $$\lim _{x \rightarrow 2n+}[x]=n, \quad f(2n)=n.$$

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