Calculate the limit of the following function in the point $$x=1$$:
$$$f(x)=\left\{\begin{array}{c} x \ \text{ si } x < 1 \\ x+1 \ \text{ si } x\geq1 \end{array} \right.$$$
See development and solution
Development:
In this case we must find the side limits, because they might not coincide
$$$\lim_{x \to 1^-}{f(x)}=\lim_{x \to 1^-}{x}=1$$$ $$$\lim_{x \to 1^+}{f(x)}=\lim_{x \to 1^+}{x+1}=1+1=2$$$
Solution:
The limit from the left is $$2$$ and from the right is $$0$$.