Two variables calculus-not too hard

1. Given the function:

$\displaystyle f(x,y) = \frac{xy^{2}}{x^{4}+y^{2}} $

Does the limit $\displaystyle \lim_{(x,y)\to(0,0)} f(x) $ exist?

2. For positive $\displaystyle \alpha , \beta $, show that:

$\displaystyle \lim_{(x,y)\to(0,0)} x^{\alpha}y^{\beta}ln(x^{4}+y^{2}) =0 $

I'll be delighted to get some guidance in these two...

In the first one I've tried to devide the function by $\displaystyle y^{2}$, but I couldn't understand how to continue...

About the second one- I think I should do something wil l'hospital's law or somehing... But I can't figure out how...

Thanks!