Question

What are the $3$ conditions of continuity?

Answer 1

Define continuity.

A function $f\left(x\right)$ is said to be continuous at $x=a$, if it satisfies the following conditions :

1. $f\left(a\right)$ should be defined.
2. Left-hand limit $=$Right-hand limit, i.e. $\underset{x\to a^{-}}{\lim }f\left(x\right)=\underset{x\to a^{+}}{\lim }f\left(x\right)$
3. $\underset{x\to a^{-}}{\lim }f\left(x\right)=\underset{x\to a^{+}}{\lim }f\left(x\right)=f\left(a\right)$