Side limits

Calculate the limit of the following function in the point $x=1$:

$$f(x)=\left\{\begin{array}{c} x \ \text{ si } x < 1 \\ x+1 \ \text{ si } x\geq1 \end{array} \right.$$

In this case we must find the side limits, because they might not coincide

$$\lim_{x \to 1^-}{f(x)}=\lim_{x \to 1^-}{x}=1$$ $$\lim_{x \to 1^+}{f(x)}=\lim_{x \to 1^+}{x+1}=1+1=2$$

The limit from the left is $2$ and from the right is $0$.