- #1

clandarkfire

- 31

- 0

## Homework Statement

Hi, I have to evaluate the following limit:

[tex]\lim_{(x,y) \to (1,0)}\frac{x*y-y}{(x-1)^2+y^2}[/tex]

## Homework Equations

I'm pretty sure I have to use the squeeze theorem.

## The Attempt at a Solution

Well, I'm pretty sure it has something to do with the fact that the top factors like this:

[tex]\lim_{(x,y) \to (1,0)}\frac{y(x-1)}{(x-1)^2+y^2}[/tex]

I'm really new to the squeeze theorem so I don't really know how to use it. I believe I have to find some function comparable to this one that is equal to it or greater than it for all values of x and y and one that is equal or less for all values of x and y. Then I have to prove that both have the same limit, so this function must have it as well.

Oh, and I suspect the limit is 0.

Can someone give me a hand, please?