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Numerade Educator

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Problem 35 Easy Difficulty

Use a Maclaurin series in Table 1 to obtain the Maclaurin series for the given function.

$ f(x) = \arctan (x^2) $

Answer

$\sum_{n=0}^{\infty}(-1)^{n} \frac{x^{4 n+2}}{2 n+1}, \quad R=1$

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Video Transcript

okay to find the MacLaurin series for the given function. So at the back Sequels to our attendant of X square Okay, we can consider X Square equals to let's say it takes two t and we can find the takes very warm community. So that is just and from one to infinity t to the power of two minus 1/2, minus one times 91 to power and minus one, which is equal to be just plugging t equals X square. So and still from one to infinity. So this is actually power of four months to over two minutes. One times they want to help them in this one, and the readers of convergence is going to be our equals to one, all right.