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 - 1.3 Exercises - Page 68: 83

Answer

$\lim\limits_{\Delta x\to0}\dfrac{3(x+\Delta x)-2-(3x-2)}{\Delta x}=3.$

Work Step by Step

$\lim\limits_{\Delta x\to0}\dfrac{3(x+\Delta x)-2-(3x-2)}{\Delta x}=\lim\limits_{\Delta x\to0}\dfrac{3x+3\Delta x-2-3x+2}{\Delta x}$ $=\lim\limits_{\Delta x\to0}\dfrac{3\Delta x}{\Delta x}=\lim\limits_{\Delta x\to0}3=3.$
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