Cases in which the limiting value of a function $f(x)$ (as $x\to c$) is not equal to $f(c)$? Can anyone state some cases such as mentioned in the title. I have tried to look for them on google and my textbook, but cant find any examples. And incidentally how can this fact be ever true? does it have something to with the function not  being defined at the limiting point $c$?

$$
\begin{align}
f(x) = \begin{cases} 
x^2-2x & \text{ if } x \not= \frac12 \\
 3 & \text{ if } x= \frac12 
\end{cases}
\end{align}
$$

