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: 56

Answer

-(2x + h)/($x^{4}$ + 2x³h + x²h²) -(w + x)/x²w²

Work Step by Step

f(x) = 1/x² f(x + h) = 1/(x + h)² = 1/(x² + 2xh + h²) [f(x + h) - f(x)]/h = {[1/(x² + 2xh + h²)] - (1/x²)}/h = = {[x² - (x² + 2xh + h²)]/[x²(x² + 2xh + h²)]}/h = = [(-2hx - h²)/($x^{4}$ + 2x³h + x²h²)]/h = = -(2x + h)/($x^{4}$ + 2x³h + x²h²) f(w) = 1/w² [f(w) - f(x)]/(w - x) = (1/w² - 1/x²)/(w - x) = [(x² - w²)/x²w²]/(w - x) = = [(x + w)(x - w)/x²w²]/(w - x) = [-(w - x)(w + x)/x²w²]/(w - x) = = -(w + x)/x²w²
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