Answer
$2$
Work Step by Step
Solve the limit $\lim\limits_{(x,y) \to (1,1)} \dfrac{x^2-y^2}{x-y}$
$\lim\limits_{(x,y) \to (1,1)} \dfrac{(x-y)(x+y)}{x-y}=\lim\limits_{(x,y) \to (1,1)}(x+y)$
Thus, $1+1=2$
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