I'm trying to show that a multivariable function is continuous at the point $(0,0)$. To do so, I'd like to show the following limit:
$\lim_{(x_1, x_2) \to (0,0)} \frac{(x_1)^3(x_2) - (x_1)(x_2)^3}{(x_1)^2 +(x_2)^2}=0$
Unfortunately, I don't have much experience with limits of multiple variables. Can anyone help?