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: 26

Answer

$\lim\limits_{x\to1}(1-[[-\dfrac{x}{2}]])=2.$

Work Step by Step

$\lim\limits_{x\to1^+}(1-[[-\dfrac{x}{2}]])=1-[[-\dfrac{1^+}{2}]]=1-(-1)=2.$ $\lim\limits_{x\to1^-}(1-[[-\dfrac{x}{2}]])=1-[[-\dfrac{1^-}{2}]]=1-(-1)=2.$ Since $\lim\limits_{x\to1^+}(1-[[-\dfrac{x}{2}]])=\lim\limits_{x\to1^-}(1-[[-\dfrac{x}{2}]])\to$ $\lim\limits_{x\to1}(1-[[-\dfrac{x}{2}]])=2.$
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