# CalcIII limit problem

1. Sep 22, 2009

### tohauz

hi.
Spse you want to find limf(x,y) as (x,y)->0.
You can use polar coordinates and get
limf(rcost,rsint) as r->0. And these limits are same.
Now, i initially thought that
1)if limf(rcost,rsint)is independent of t,then limit
exists and is equal tolimf(x,y) as (x,y)->0.
2)If it depends on t, then limit DNE.
But, i did this limits using these methods and got different answers:
limit(xy^{4}/x^{2}+y^{8}) as (x,y)->0.
So if you try x=y^{4} path, you get 0.5
y=0 path, you get 0. So DNE
if you convert into polar, you get zero.

Where is the mistake??