Define continuity of a function at a point. - Vidyadip

Question

Define continuity of a function at a point.

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Answer

Continuity at a point:
A function f(x) is said to be continuous at a point x = a of its domain, $\lim\limits_{{\text{x}}\rightarrow\text{a}}\text{f(x)}=\text{f(a)}$
Thus, f(x) is continuous at $\text{x}=\text{a}\Leftrightarrow\lim\limits_{{\text{x}}\rightarrow\text{a}}\text{f(x)}=\text{f}(\text{a})\Leftrightarrow\lim\limits_{{\text{x}}\rightarrow\text{a}^-}\text{f(x)}=\lim\limits_{{\text{x}}\rightarrow\text{a}^+}\text{f(x)}=\text{f}(\text{a})$

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