Hi fabio010,I know that the solution is correct. But i do not know if i resolved it in the correct way.
The images are attached.
You are assuming that the limit exists and so the limits may be taken in any order.Thanks a lot for correct the limits.
First of all sorry for the writing, it is so ugly because i wrote it in paint.
Next time i am going to try to use LATEX.
The last two, in first one i just used the notable limit of e^k
the second one is wrong.... x^2/(x^2+y^2) is not equal to 1/(x+y^2) -_-
Still does not look rightWhen all paths get as result the same limit, we can use the polar coordinates too prove that the limit is limit of all paths, right?