Use multiplication or division of power series to find the first three nonzero terms in the maclaurin series for the given function. (Enter your answers as a comma-separated list.) y=(e^-x^2)cosx

1 , - ( 3x^2/2), + (25x^4/24).

Step-by-step explanation:

We are given the following information:

y = (e^-x^2)cosx.

STEP ONE: Write out the power series out(either by deriving it or otherwise).

If you check the power series table, you will get the power series for the two functions that is cos x and e^-x^2.

e^-x^2 = 1 - (x^2) + ( x^4/2! ) - (x^6/3!) +...

Cos x = 1 - (x^2/2!) + x^4/4!) + (x^6/6!) -...

STEP TWO: Multiply both the power series of e^-x^2 and Cos x together because we are to determine or find the first three nonzero terms in the maclaurin series for the given function.

1 - (x^2) + ( x^4/2! ) - (x^6/3!) +... - 1 - (x^2/2!) + x^4/4!) + (x^6/6!) -...

= 1 - ( 3x^2/2) + (25x^4/24).

= 1, - ( 3x^2/2) , + (25x^4/24) => comma- separated list.

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