Finding the Limit of a Multivariable Function at (0,0)

[ahhppull]

Homework Statement

lim of (y^2)(sin^2x) /(x^4+y^4) as (x,y) approaches (0,0)

Homework Equations

The Attempt at a Solution

I got the limit as (x,y) approaches (0,y) and as (x,y) approaches (x,0), and it equals 0. But now I'm unsure of what to to next. I think it was the limit as (x,y) approaches (x,x) when x=y, but i get sin^2x / 2x^2

 

[szynkasz]

$$\lim_{x\to 0}\frac{\sin^2x}{2x^2}=\frac{1}{2}\lim_{x\to 0}\left(\frac{\sin x}{x}\right)^2=\frac{1}{2}$$