CONTINUITY OF FUNCTIONS OF ONE VARIABLE

A function $f(x)$ is defined on an open interval around $c$. We say that the function $f(x)$ is continuous at $c$ if the following are true

• Limit of $f(x)$ at $x=c$ exists
• Function is defined at $x=c$
• $\lim_{x\rightarrow c}f(x)=f(c)$

For a function to be continuous at a point, the function should $(1)have a limit at that point, $(2)$ be defined at that point and $(3)$ the value of the function at that point should be equal to the limit of the function at that point.