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

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Answer 1 · 2015-05-20T14:05:36

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

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

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