# Homework Help: Expand f(x,y) = y^2/x^2

1. Feb 11, 2006

### darkar

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

2. Feb 11, 2006

### Zurtex

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

3. Feb 11, 2006

### darkar

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

4. Feb 11, 2006

### 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)

Last edited by a moderator: Feb 12, 2006
5. Feb 11, 2006

### daveb

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

6. Feb 11, 2006

### Hurkyl

Staff Emeritus
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!