Calculus, 10th Edition (Anton)

Published by Wiley
ISBN 10: 0-47064-772-8
ISBN 13: 978-0-47064-772-1

Chapter 0 - Before Calculus - 0.2 New Functions From Old - Exercises Set 0.2: 55

Answer

-1/(x² + xh) -1/xw

Work Step by Step

f(x) = 1/x f(x + h) = 1/(x + h) [f(x + h) - f(x)]/h = [1/(x + h) - 1/x]/h = {[x - (x + h)]/[x(x + h)]}/h = = [-h/(x² + xh)]/h = -1/(x² + xh) f(w) = 1/w [f(w) - f(x)]/(w - x) = (1/w - 1/x)/(w - x) = [(x - w)/xw]/(w - x) = = -1/xw
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