# Question #82505

Mar 1, 2017

See below.

#### Explanation:

Choosing a path such that $y = \lambda x$ we have

$\frac{x y}{{x}^{2} + {y}^{2}} = \frac{{x}^{2} \lambda}{{x}^{2} \left(1 + {\lambda}^{2}\right)} = \frac{\lambda}{1 + {\lambda}^{2}}$

depending on the parameter $\lambda$.

Concluding

${\lim}_{\left(x \to 0\right) \left(y \to 0\right)} \frac{x y}{{x}^{2} + {y}^{2}}$ does nor exist.