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Problem 48 Hard Difficulty
Find the Maclaurin series of $ f $ (by any method) and its radius of convergence. Graph $ f $ and its first few Taylor polynomials on the same screen. What do you notice about the relationship between these polynomials and $ f? $
$ f(x) = \tan^{-1} (x^3) $
Answer
$\sum_{n=0}^{\infty}(-1)^{n} \frac{x^{6 n+3}}{2 n+1}, \quad R=1$
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