Multivariable function limit How to approach this: $\lim\limits_{(x,y)\to(0,0)}\frac{x^2y}{x^2+y}$?
Been able to grind $\lim\limits_{(x,y)\to(0,0)}\frac{x^2y}{x^2+y^2}$, it is in(link) finnish, but formulas and idea should be selfevident. However $\dot +y$ instead of $\dots+y^2$ in divisor confuses me.
Or am I thinking in completely wrong direction?

Here's another approach
$$\lim\limits_{(x,y)\to(0,0)}\frac{x^2y}{x^2+y}$$
Using polar coordinates, we have
$$\lim\limits_{r\to 0^+}\frac{r^2\cos^2\phi\sin\phi}{r\cos^2\phi+\sin\phi}$$
Now lets attempt to find bounds that are independent of $\phi$
$$\frac{r^2\left|\cos^2\phi\sin\phi\right|}{\left|r\cos^2\phi+\sin\phi\right|}\leq\frac{r^2}{\left|r\cos^2\phi+\sin\phi\right|}$$
Since this limit is dependent on $\phi$, we can conclude that
$$\lim\limits_{(x,y)\to(0,0)}\frac{x^2y}{x^2+y}=\mbox{non existent}$$
