Question

Define continuity of a function at a point.

Answer 1

Continuity at a point:

A function $f\left(x\right)$ is said to be continuous at a point x = a of its domain, iff $\underset{x\to \mathrm{a}}{\lim }f\left(x\right)=f\left(a\right)$.
$$\begin{gathered} \mathrm{Thus},f\left(x\right)\mathrm{is}\mathrm{continuous}\mathrm{at}x=a. \\ \iff \underset{x\to a}{\lim }f\left(x\right)=f\left(a\right)\iff \underset{x\to a^{-}}{\lim }f\left(x\right)=\underset{x\to a^{+}}{\lim }f\left(x\right)=f\left(a\right) \end{gathered}$$