hi.(adsbygoogle = window.adsbygoogle || []).push({});

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??

Thanks in advance

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# CalcIII limit problem

**Physics Forums | Science Articles, Homework Help, Discussion**