# For a continuous function (let's say f(x)) at a point x=c, is f(c) the limit of the function as x tends to c? Please explain.

Oct 13, 2016

Yes, by definition

#### Explanation:

One commonly used definition for a function $f$ being continuous at a point $c$ is that $f$ is continuous at $c$ if

${\lim}_{x \to c} f \left(x\right) = f \left(c\right)$

(note that this definition implicitly requires ${\lim}_{x \to c} f \left(x\right)$ and $f \left(c\right)$ to exist)

As the question $f \left(x\right)$ being continuous at $c$ as a given, that means all necessary conditions for $f \left(x\right)$ being continuous at $c$ must be true, in particular, ${\lim}_{x \to c} f \left(x\right) = f \left(c\right)$.