## Calculus 10th Edition

For a limit to exist, it should attain the same value from both sides. While $f(x)=3$ at $x=2,$ the limit attains two values when approaching $x=2$. You get the limit equal to $3$ from the left and equal to $0$ from the right, hence the limit doesn't exist and $\lim\limits_{x\to2}f(x)\ne3$.