VTRMC 2005 Problem 5

Define $f(x,y)=\frac{xy}{x^2+y^2\ln(x^2)^2}$ if $x\ne0$ , and $f(0,y)=0$ if $y\ne0$ . Determine whether $\lim_{(x,y)\to(0,0)}f(x,y)$ exists, and find its value is if the limit does exist.