Question

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.

Answer 1

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->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)`.