Find
lim as (x,y) goes to (0,0) of
(e^(-x^2-y^2)-1)/(x^2+y^2).
lim (e^-u^2-1)/u^2
= lim (-2u e^-u^2)/2u = -1
Now let u^2 = x^2+y^2
lim as (x,y) goes to (0,0) of
(e^(-x^2-y^2)-1)/(x^2+y^2).
= lim (-2u e^-u^2)/2u = -1
Now let u^2 = x^2+y^2