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 $f(x,y)=\frac{x^2}{x^2+y^2-x}$, Continuous on (0,0), if not say what kind of discontinuity is it.
Clearly $f(0,0)=\frac{0^2}{0^2+0^2-0}$, its a form of indeterminate. So we go to the limit. $\lim_{(x,y) \to (0,0)} \frac{x^2}{x^2+y^2-x}$
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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