Chapter 14 - Partial Derivatives - 14.2 Exercises - Page 923: 13

$0$

We can see that the limit along any line through (0,0) is 0, as well as along other paths throug (0,0) such as x=y^{2} and y =x^{2} so we suspect that the limit exist and equals 0. We use the Squeeze Theorem to proveour assertion.