# Limits of multivariable functions

1. May 2, 2014

### Feodalherren

1. The problem statement, all variables and given/known data

The limit as x,y → 0

$\frac{y^{2}Sin^{2}x}{x^{4}+y^{4}}$

2. Relevant equations

3. The attempt at a solution

There are pretty straight forward but I have a general question about them. So say in the function above I let y=x and let x approach 0.

I get 0/0 - inconclusive. Can I fall back on single variable calculus and use L'Hospital's rule to find the limit? For some reason my gut tells me no.

2. May 2, 2014

### Zondrina

If you approach along a straight line, you would need to use L'Hospital's rule to find the limit. What happens if you approach along a parabola? Compare that to approaching along a straight line. What can you conclude?