Thomas' Calculus 13th Edition

Published by Pearson
ISBN 10: 0-32187-896-5
ISBN 13: 978-0-32187-896-0

Chapter 10: Infinite Sequences and Series - Section 10.9 - Convergence of Taylor Series - Exercises 10.9 - Page 625: 38


$\lt 0.0026$

Work Step by Step

Recall the Taylor series for $\cos x=1-\dfrac{x^2}{2}+\dfrac{ x^3}{3}-....$ We can see that the term $1-\dfrac{x^2}{2}$ is too small by the Alternating Series Estimation Theorem. Therefore, the error is less than $\dfrac{(0.5)^4}{24} \lt 0.0026$ by the Alternating Series Estimation Theorem.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.