Question

What happens to a function f (x) at x = a, if $\underset{x\to a}{\lim }$ f (x) = f (a)?

Answer 1

If $f\left(x\right)$ is a function defined in its domain such that $\underset{x\to \mathrm{a}}{\lim }f\left(x\right)=f\left(a\right)$, then $f\left(x\right)$ becomes continuous at $x=a$.