We know that to make the limit of a function $$f(x)$$ at point $$p$$ involves seeing all the values of the function $$f(x)$$ when we are located very close to $$x=p$$, but not exactly on $$p$$. This means that we are approximating $$x=p$$, but how? From the right? From the left? We are going to specify the limit definition:
Limit from the left of $$f(x)$$ in $$x=p$$:
$$$L^-=\lim_{x \to p^-}{f(x)}$$$
Limit from the right of $$f(x)$$ in $$x=p$$:
$$$L^+=\lim_{x \to p^+}{f(x)}$$$
And if these two limits coincide $$(L^-=L^+)$$, then we say that:
$$$L=L^+=L^-=\lim_{x \to p}{f(x)}$$$
Let's take the function $$f(x)=\left\{\begin{array}{c} 0 \ \text{ si } x < 2 \\ 1 \ \text{ si } x\geq2 \end{array} \right.$$ and we will look for the side limits at $$x=2$$.
Limit from the left:
$$$L^-=\lim_{x \to 2^-}{f(x)}=\lim_{x \to 2^-}{0}=0$$$
Limit from the right:
$$$L^+=\lim_{x \to 2^+}{f(x)}=\lim_{x \to 2^+}{1}=1$$$
and nevertheless, the function in $$x=2$$ is $$1$$.
When a limit is computed, what can occur is that a function increases a great deal and we go so far as to say that the value of a limit is infinite.
Let's remember that we symbolize infinity with the symbol: $$\infty$$.