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: 85

Answer

$\lim\limits_{\Delta x\to0}\dfrac{(x+\Delta x)^2-4(x+\Delta x)-(x^2-4x)}{\Delta x}=2x-4.$

Work Step by Step

$\lim\limits_{\Delta x\to0}\dfrac{(x+\Delta x)^2-4(x+\Delta x)-(x^2-4x)}{\Delta x}$ $=\lim\limits_{\Delta x\to0}\dfrac{x^2+2x(\Delta x)+(\Delta x)^2-4x-4\Delta x-x^2+4x}{\Delta x}$ $=\lim\limits_{\Delta x\to0}\dfrac{\Delta x(2x-4+\Delta x)}{\Delta x}$ $=\lim\limits_{\Delta x\to0}(2x-4+\Delta x)=2x-4+0=2x-4.$
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