Answer
$\lim\limits_{x \to a} f(x) = b$
Work Step by Step
$\lim\limits_{x \to a}b-|x-a| \leq\lim\limits_{x \to a}f(x)\leq\lim\limits_{x \to a}b+|x-a|$
$b-|a-a|\leq\lim\limits_{x \to a}f(x)\leq b+|a-a|$
$b\leq\lim\limits_{x \to a}f(x)\leq b$
Therefore, $\lim\limits_{x \to a}f(x) = b$
