<s>[INST] Two-variable limit question $\lim\limits_{(x,y)\rightarrow (0,0)} \dfrac{x^2y^2}{(x^2+y^4)\sqrt{x^2+y^2}}$
How to solve this two-variable limit? Thanks :D
 [/INST] This might also be an approach:
$$0 \le \frac{x^2y^2}{(x^2 + y^4)\sqrt{x^2 + y^2}} \le \frac{x^2y^2}{x^2\sqrt{x^2+y^2}} \le \frac{y^2}{\sqrt{y^2}} \le |y|$$
So, since $(x,y) \to (0,0)$ then $|y| \to 0$ and passing to a limit we obtain that the initial expression goes to 0.
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