Calculus (3rd Edition)

Published by W. H. Freeman
ISBN 10: 1464125260
ISBN 13: 978-1-46412-526-3

Chapter 11 - Infinite Series - 11.7 Taylor Series - Exercises - Page 589: 68



Work Step by Step

Since we have$$ x^{4}-\frac{x^{12}}{3}+\frac{x^{20}}{5}-\frac{x^{28}}{7}+\cdots\\ =x^{4}-\frac{(x^{4})^{3}}{3}+\frac{(x^{4})^{5}}{5}-\frac{(x^{4})^{7}}{7}+\cdots\\ $$ Then by using Table 2, we see that this is a Maclaurin series of the function $$\tan^{-1}(x^4).$$
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