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 10.10 - The Binomial Series and Applications of Taylor Series - Exercises 10.10 - Page 633: 26


$| Error| \lt 0.00064$

Work Step by Step

Integrate the integral with respect to $ x $ as follows: $ f(x)=\int_0^{x} t^2 e^{-t^2} \space dt \space \\=\int_0^{x} [t^2-t^4+\dfrac{t^6}{2 !} -\dfrac{t^{8}}{3!}-...] \space dt \\ =\dfrac{x^3}{3}-\dfrac{x^{5}}{5}+\dfrac{x^{7}}{7 \cdot 2!}-\dfrac{x^{9}}{9 \cdot 3!}+\dfrac{x^{11}}{11 \cdot 4!} ....$ Now, the error can be found as follows: $| Error| \lt \dfrac{1}{13\cdot 5 !} \approx 0.00064$ and $| Error| \lt 0.00064$
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