Answer
$\lim\limits_{x\to2}f(x)=0.$
Work Step by Step
$\lim\limits_{x\to2^-}f(x)=\lim\limits_{x\to2^-}(x-2)^2=(2^--2)^2=0.$
$\lim\limits_{x\to2^+}f(x)=\lim\limits_{x\to2^+}(2-x)=(2-2^+)=0.$
Since $\lim\limits_{x\to2^+}f(x)=\lim\limits_{x\to2^-}f(x)\to\lim\limits_{x\to2}f(x)$ exists and is equal to $0.$
