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?

Question

For a continuous function (let&#039;s say f(x)) at a point x=c, is f(c) the limit of the function as x tends to c?

Zackary Galloway · Accepted Answer

Yes, by definitionExplanation:One commonly used definition for a function f being continuous at a point c is that f is continuous at c if            lim              x        →        c                    f              (        x        )              =          f              (        c        )            (note that this definition implicitly requires              lim              x        →        c                    f              (        x        )             and f(c) to exist)As the question f(x) being continuous at c as a given, that means all necessary conditions for f(x) being continuous at c must be true, in particular,            lim              x        →        c                    f              (        x        )              =          f              (        c        )

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?

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