Answer
$ e^2$
Work Step by Step
We are given $ \lim\limits_{(x,y) \to (2,5)}f(x,y)=3$ and $ \lim\limits_{(x,y) \to (2,5)}g(x,y)=7$, then we have
$$ \lim\limits_{(x,y) \to (2,5)}e^{f(x,y)^2-g(x,y)}=e^{\lim\limits_{(x,y) \to (2,5)}f(x,y)^2-\lim\limits_{(x,y) \to (2,5)}g(x,y)}\\=e^{3^2-7}=e^2.$$
