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: 61

Answer

$\lim\limits_{\Delta x\to 0}=\dfrac{(x+\Delta x)^2-2(x+\Delta x)+1-(x^2-2x+1)}{\Delta x}=2x-2.$

Work Step by Step

$\lim\limits_{\Delta x\to 0}=\dfrac{(x+\Delta x)^2-2(x+\Delta x)+1-(x^2-2x+1)}{\Delta x}$ $=\lim\limits_{\Delta x\to 0}\dfrac{x^2+2x(\Delta x) +(\Delta x)^2-2x-2\Delta x+1-x^2+2x-1}{\Delta x}$ $=\lim\limits_{\Delta x\to 0}\dfrac{\Delta x(\Delta x+2x-2)}{\Delta x}$ $=\lim\limits_{\Delta x\to 0}\Delta x+2x-2=2x-2.$
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