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 

\[\lim_{x \to a} f\left( x \right) = f\left( a \right)\]

\[\text{ Thus,}  f\left( x \right) \text{ is continuous at }  x = a . \]
\[ \Leftrightarrow \lim_{x \to a} f\left( x \right) = f\left( a \right) \Leftrightarrow \lim_{x \to a^-} f\left( x \right) = \lim_{x \to a^+} f\left( x \right) = f\left( a \right)\]