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: 28

Answer

$\lim\limits_{\Delta x\to 0}\dfrac{\cos{(\pi+\Delta x)}+1}{\Delta x}=0.$

Work Step by Step

$\lim\limits_{\Delta x\to 0}\dfrac{\cos{(\pi+\Delta x)}+1}{\Delta x}$ $=\lim\limits_{\Delta x\to 0}\dfrac{\cos{\pi}\cos{\Delta x}-\sin{\pi}\sin{\Delta x}+1}{\Delta x}$ $=\lim\limits_{\Delta x\to 0}\dfrac{1-\cos{\Delta x}}{\Delta x}=0.$
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