University Calculus: Early Transcendentals (3rd Edition)

Published by Pearson
ISBN 10: 0321999584
ISBN 13: 978-0-32199-958-0

Chapter 9 - Section 9.9 - Convergence of Taylor Series - Exercises - Page 542: 40


$|\space Error| \lt 1.25 \times 10^{-5}$

Work Step by Step

The Binomial series for $\sqrt{1+x}$ can be defined as: $\sqrt{1+x}=1+\dfrac{x}{2}-\dfrac{x^2}{8}+\dfrac{x^3}{16}-.....$ By the Alternating Series Estimation Theorem, the error can be calculated as: $|Error| \lt |\dfrac{-x^2}{8}| $ or, $|Error| \lt \dfrac{(0.01)^2}{8} $ or, $|\space Error| \lt 1.25 \times 10^{-5}$
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