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 - Practice Exercises - Page 553: 78



Work Step by Step

The Taylor series for $\cos x $ can be defined as: $\cos x=1-\dfrac{x^2}{2!}+\dfrac{ x^4}{4!}-....$ Now, $\lim\limits_{y \to 0} \dfrac{y^2}{\cos y-\cos h y}=\lim\limits_{y \to 0} \dfrac{y^2}{(1-y^2/2+y^4/4!)-(1-y^2/2!+y^4/4!)}$ or, $=\lim\limits_{y \to 0} \dfrac{y^2}{-1-\dfrac{2y^4}{6!}-.......}$ or, $=\dfrac{1}{-1-1-0-....}$ or, $=-1$
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