Expanding the Function f(x,y) around (1,-1): What's the Easy Way?

[darkar]

How do u expand f(x,y) = y^2/x^2 about the point (1,-1) ? up to and including quadratic term?

 

[Zurtex]

How do u expand f(x,y) = y^2/x^2 about the point (1,-1) ? up to and including quadratic term?

Have you ever used the taylor series on multi-variable functions before?

 

[darkar]

Not really, how? Have only done one variable so far.

 

[HallsofIvy]

The general term in a Taylor's series for f(x,y) about the point (a,b) is
$$\frac{1}{(m+n)!}\frac{\partial^m f}{\partial x^m}\frac{\partial^n f}{\partial y^n}(x- a)^m(y- b)^n$$

(edited. Thanks, daveb)

 

[daveb]

Shouldn't that (x - b)^n be (y - b)^n?

 

[Hurkyl]

Bah, everybody likes to do it the hard way. f(x, y) is just a product of two things whose Taylor series you already know!