Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 4 - Applications of the Derivative - 4.1 Linear Approximation and Applications - Exercises - Page 172: 4



Work Step by Step

$ f(x)=\frac{1}{x+1}$, $ a=3$, $\Delta x=0.02$ and $ f'(x)=\frac{-1}{(x+1)^{2}}$ (Using the reciprocal rule for differentiation) Recall: $ f(a+\Delta x)-f(a)\approx f'(a)\Delta x $ $\implies f(3+0.02)-f(3)\approx f'(3)\Delta x=\frac{-1}{(3+1)^{2}}\times0.02=-0.00125$
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