Question

How do you use continuity to evaluate the limit `(e^(x^2) - e^(-y^2)) / (x + y)` as `(xy)` approached `(1,1)`?

Answer 1

The continuity of the function at the point means you can just plug in the point to evaluate the limit:

`lim_{(x,y)->(1,1)}(e^{x^2}-e^{-y^2})/(x+y)=(e-e^{-1})/2\approx 1.1752`