# Limit and Continuity

1. Sep 27, 2012

### ahhppull

1. The problem statement, all variables and given/known data
lim of (y^2)(sin^2x) /(x^4+y^4) as (x,y) approaches (0,0)

2. Relevant equations

3. 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

2. Sep 27, 2012

### szynkasz

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