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: 38


$\lt 0.0026$

Work Step by Step

The Taylor series for $\cos x $ can be defined as: $\cos x=1-\dfrac{x^2}{2}+\dfrac{ x^3}{3}-....$ Since, the term $1-\dfrac{x^2}{2}$ is too small by the Alternating Series Estimation Theorem. So, the error is less than $\dfrac{(0.5)^4}{24} \lt 0.0026$ by the Alternating Series Estimation Theorem.
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