## Calculus (3rd Edition)

Published by W. H. Freeman

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

#### Answer

$$\tan^{-1}(x^4).$$

#### 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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