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Find the MacLaurin Series

Find the MacLaurin Series of f(x) = x3sin(x)

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Andre W. | Friendly tutor for ALL math and physics coursesFriendly tutor for ALL math and physics ...
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The MacLaurin series of sin(x) is ∑n=0 (-1)n x2n+1/(2n+1)!, so the series for x3sin(x) is
n=0 (-1)n x2n+4/(2n+1)!
It converges everywhere.