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: 41


$\lt 1.87 \times 10^{-4}$

Work Step by Step

Write the Taylor series for $ e^x =1+x +\dfrac{x^2}{2}+\dfrac{ x^3}{6}-....$ Apply the Remainder Estimation Theorem to calculate the error. $|R_n(x)| \leq M \dfrac{|x-a|^{n+1}}{(n+1)!}$ $\implies |R_2(x)| \leq |\dfrac{e^ex^3}{3!}| $ and Error $ \lt \dfrac{3^{0.1} \cdot (01)^{3} }{3!} \lt 1.87 \times 10^{-4}$
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