Limit with two-variable function $f(x,y)=\frac{\ln(x+e^y)}{\sqrt{x^2+y^2}}, \;x\geqslant0,\; x^2+y^2\neq0$. Find the limit when $(x,y) \to (0,0)$. I tried it with Maclaurin and then polar change but can't find it.

Hint: Notice that $$f(0, y) = \frac{\ln(e^y)}{\sqrt{y^2}} = \frac{y}{|y|}.$$
