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## Homework Statement

Find the third degree Taylor polynomial about the origin of

[itex]f(x,y) = \frac{\cos(x)}{1+xy}[/itex]

## Homework Equations

## The Attempt at a Solution

From my ventures on the Internet, this is my attempt:

I see that

[itex]\cos(x) = 1 - \frac{1}{2}x^2 + \frac{1}{4!}x^4 - \cdots[/itex]

[itex]\frac{1}{1+x} = 1 - x + x^2 - x^3 + \cdots[/itex]

and so

[itex]\frac{1}{1+(xy)} = 1 - xy + x^2y^2 - x^3y^3 + \cdots[/itex]

Therefore, in multiplying them out,

[itex]f(x,y) = \frac{\cos(x)}{1+xy} = 1 - xy + x^2y^2 - x^3y^3 - x + x^2y - x^3y^2 + \cdots[/itex]

And I suppose that would be my answer.

Do I have the right idea?

Thanks in advance.

EDIT: Oops! I didn't substitute [itex](x,y) = (0,0)[/itex]. So, in doing that, I should get precisely [itex]1[/itex].

*That*is my answer.

EDIT: But [itex]1[/itex] doesn't seem right...

EDIT: I think I am getting confused. Pretty sure the product above would be the answer, D=

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