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WZ
Numerade Educator

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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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Video Transcript

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