Answer
$\lim\limits_{(x,y) \to (1,-1)} (e^{-xy} cos(x+y)) = e$
Work Step by Step
$-xy$ is continuous everywhere.
$x + y$ is continuous everywhere.
$e^{-xy}$ and $cos(x+y)$ are continuous everywhere.
Therefore, we can substitute the values of x and y directly into the fuction.
$\lim\limits_{(x,y) \to (1,-1)} (e^{-xy} cos(x+y)) = e^{-(1)(-1)}cos(1 - 1) = e^1cos(0) = e$
