Question

Is the statement "if limit of f(x)=L as x approaches c, then f(c)=L" a true or false statement?

Answer 1

It's a false statement.

First we have to suppose that `L` is finite, Then `f(x)` may not even be defined for `x=c` as in the case:

`lim_(x->0) sinx/x = 1`

In fact the property:

`lim_(x->c) f(x) = f(c)`

is what defines a function that is continuous in `x=c`.

In other words the statement is equivalent to saying that `f(x)` is continuous in `x=c` and not all functions are continuous in their entire domain.