Problem

Find the first three nonzero terms of the Maclaur…

Problem 38 Easy Difficulty

Find the first three nonzero terms of the Maclaurin series for each function.
$$f(x)=x \sin ^{2} x$$

Answer

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Calculus 2 / BC

University Calculus: Early Transcendentals

Chapter 9

Infinite Sequences and Series

Section 8

Taylor and Maclaurin Series

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Video Transcript

So the model in Syria's generated by sign of eggs is equal to and the Sigma from an equal zero to infinity Negative 12 part end about a bite to impossible on factorial times x the power of to in plus one This serious converges on negative infinity to infinity he series generated by, um X time Senate X squared is going to be so let me just read it. Also f X equals x times, um, sort of X and in squared. So you're going to replace son of ex with what we found right up here. And so it is gonna look like X times. So we're just refining the, uh, serious. So an equal zero to infinity Negative wants the party end by the bite to and plus one factorial times exit, part two in plus one. Remember, there's a squared right here, so we're going to add a squared. And so once we simplify, we get X cubed minus 1/3 x tooth there plus two divided by 45 times x, the seventh minus one divided by 3 15 Excellent. Nine plus dot dot Doc, This convergence on negative infinity to infinity and so here are the first few terms. The first few terms we're going to be X cubed minus one. That expects, plus to to buy the 45 access seventh. So right up here, These are the 1st 3 terms, and the interval of convergence is negative. Infinity to infinity.

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