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 - Review Exercises: 48

Answer

$\lim\limits_{x\to4}[[x-1]]$ does not exist.

Work Step by Step

$\lim\limits_{x\to4^-}[[x-1]]=[[4^--1]]=[[3^-]]=2.$ $\lim\limits_{x\to4^+}[[x-1]]=[[4^+-1]]=[[3^+]]=3.$ Since $\lim\limits_{x\to4^-}[[x-1]]\ne\lim\limits_{x\to4^+}[[x-1]]\to\lim\limits_{x\to4}[[x-1]]$ does not exist.
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