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: 60

Answer

$f(x)$ has an a discontinuity at every integer value of $x.$ These discontinuities are not removable.

Work Step by Step

Using Theorem $1.11:$ Since $f(x)=5$ is continuous for all values of x, but $g(x)=[[x]]$ is continuous for all non-integer values of $x$; $f(x)-g(x)$ is discontinuous for all integer values of x. These discontinuities (jump) are irremovable.
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