Question

Question #82505

Answer 1

See below.

Explanation:

Choosing a path such that `y = lambda x` we have

`(x y)/(x^2+y^2) = (x^2 lambda)/(x^2(1+lambda^2)) = lambda/(1+lambda^2)`

depending on the parameter `lambda`.

Concluding

`lim_((x->0)(y->0))(x y)/(x^2+y^2)` does nor exist.