Find $\lim\limits_{(x,y)\to (0,0)}{\frac{e^{x}+y-1}{x+y}}$

Question

Find $$\lim_{(x,y)\to (0,0)}{\dfrac{e^{x}+y-1}{x+y}}$$

I tried with different trajectories and I always get that the limit is $1$, but I cannot prove it, any help?

Answer 1

Hint: Along the path $$ y=1-e^x $$ we get the limit is $0$. However, along the path $$ x=0 $$ the limit is $1$.