Question

How do you prove a function is continuous?

Answer 1

To prove that a function is continuous at a point $c$, the following are the factors that needs to be checked:

$\mathbf{1}\mathbf{.}\mathbf{}\mathit{f}\mathbf{\left(}\mathit{c}\mathbf{\right)}$ must be defined.

$2.$There must be an existence of the limit of the function $f$should approach the value$c.$

$3.$ The value of $c$ at function and the limit of $x$ approaching $c$ must be the same.

$\mathbf{4}\mathbf{.}\mathbf{}\mathit{f}\mathbf{\left(}\mathit{x}\mathbf{\right)}$ must exist.