I have the following problem:(adsbygoogle = window.adsbygoogle || []).push({});

find the first 3 non-zero terms in the Maclaurin series for the function:

e^{-x2 }+ Cos[x]

I know in this case, the series behave like polynomials and I have done the following. The left expression is the first 3 terms of the e portion of the problem, and the second expression is the first 3 terms of Cosx.

(1 - x^{2}+ x^{4}/2)(1 - x^{2}/2 + x^{4}/24)

this =

1 - x^{2}/2 + x^{4}/24 - x^{2}- x^{4}/2 - x^{6}/24 + x^{4}- x^{6}/4 + x^{8}/48

How do I know which terms are the "first 3 non-zero terms" of this series?

Thanks - the answer is attached, I just don't understand how the polynomial, after multiplied out is consolidated at the end.

Jeff

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# Multiplication of Maclaurin Series

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