Why does the following limit not exist? The limit is $$\lim\limits_{(x,y)\to(0,0)}\frac{\sqrt y}{\sqrt x}$$  I thought it was 1.
Also what about $$\lim\limits_{(x,y)\to(0,0)}\frac{ y}{ x}$$

If any of the limits existed, then all the sublimits (for each case) would coincide. So take the limits along the parabolas $y=kx^2$ to find different sublimits.
