Limit of multivariable function $f(x,y) = {(x^2+y^2)}^{x^2y^2}$ $$f(x,y) = {(x^2+y^2)}^{x^2y^2}$$
I need to find the limit at (0,0) point
I applied the exponent rule and got $$e^{x^2y^2ln(x^2+y^2)}$$
and now with chain rule, I need to find the limit of $${x^2y^2ln(x^2+y^2)}$$
and how? :D
There isn't L'Hôpital's rule for multivariable function, right?

Observe immediately that the function is symmetric: that is $$f(x,y)=f(y,x)$$
Then, you can set $y=y(x)$ as any function so that $x\to 0\implies y\to 0$ and calculate $$\lim_{x\to 0}f(x,y(x))$$ as a limit of one variable.
Some examples of $y(x)$ are $y(x)=0,y(x)=kx, k\in \Bbb R^+$
