How to calculate the limit of the following function?

Question

How can I calculate the limit of the following function?

$$\lim_{(x,y)\to(0,0)}\frac{-|x+y|}{e^{x^2}{^{+2xy+y^2}}}$$

Answer 1

Hint.

$(x+y)^2=x^2+2xy+y^2$ and $a^2=|a|^2$.

Answer 2

the exponential function is continuos so you can pull the limit inside and thus get $$\exp\left({\lim_{(x,y)\to0}\frac{-|x+y|}{|x+y|^2}}\right) .$$ I presume you can go on from here by yourself