University Calculus: Early Transcendentals (3rd Edition)

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

Chapter 9 - Section 9.10 - The Binomial Series and Applications of Taylor Series - Exercises - Page 550: 48


$$\cos (3x)$$

Work Step by Step

The Taylor series for $\cos x $ can be defined as: $\cos x=1-\dfrac{ x^2}{2!}+\dfrac{x^4}{4!}-....$ Consider the given series: $\\=1-\dfrac{3^2 \cdot x^2}{2!}+\dfrac{3^4 \cdot x^4}{4!} - \dfrac{3^6 \cdot x^6}{6!}+.....\\=1-\dfrac{1}{2!}(3x)^2+( \dfrac{1}{4!}) (3x)^4-......\\=\cos (3x)$
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