Well, I've been calculating some limits of several variable functions and got confused with something: everybody knows that if taking a path the limit depends on the path chosen then the limit doesn't exist. But, if you consider the limit(adsbygoogle = window.adsbygoogle || []).push({});

lim (x,y) -> (0,0) [itex]\frac{y^{2}x}{x^{2}+y^{2}}[/itex]

that can be easily calculated( function that converges to 0 multiplied by limited function ). ALthough, if you choose the path

y=[itex]\sqrt{\frac{c}{x-c}}x[/itex]

you'll end up with a limit equals to c, in other words, it depends oof the path you choose what would be enough for us to say the limit doesn't exist. The problem is we know it exists and my question is: did i forget to consider any important hypothesis or condition? How can the path test be applied correctly then?

I appreciate your attention.

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

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

# Two-Path Test:Fail?

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