Wednesday, 16 October 2013

multivariable calculus - Can wolframAlpha be wrong on this vector limit?

We had a homework on multivariable analysis, and there was this problem and the teacher said that we didnt trust wolfram but I'm not convinced on it, because of this.



Is f(x,y)=x2x2+y2x, Continuous on (0,0), if not say what kind of discontinuity is it.



Clearly f(0,0)=0202+020, its a form of indeterminate. So we go to the limit. lim(x,y)(0,0)x2x2+y2x
I get 0, on some few cases, but i cant prove that its 0, but i "asked" wolfram and he said its 0, but some other of my class mates say that wolfram gave a non existing limit, or when they refreshed the site, it gave a different answer(which i think its very odd)



Is wolfram possibly wrong, or the limit there is 0.

I got a little far on proving that the limit does exist but, i could be wrong, because i cant finish it.



Any ideas on that limit?

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