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 10.8 - Taylor and Maclaurin Series - Exercises 10.8 - Page 619: 44


$L(x)=1$ and $Q(x)=1+\dfrac{x^2}{2!}$

Work Step by Step

Differentiate the given function $f(x)$ as follows: $f'(x)= \sinh x ; \\f''(x)= \cosh x$ Now $ f(0)=1; \\ f'(0)=1; \\ f''(0)=1$ Therefore, $L(x)=f(0)+xf'(0)=1$ and $Q(x) =f(0) x +xf'(0) +\dfrac{x^2 f''(0)}{2!}=1+\dfrac{x^2}{2!}$
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