Question

given an arbitrary function f, if lim (x -> 2) f(x) = 5, what is f(2)

Answer 1

\[\lim_{x \rightarrow 2} f(x) = 5\] what is f(2). The answer is Not enough information to determine f(2). why is this? isn't it 5?

Answer 2

Hmm yah it seems like you don't have enough information here. Maybe we're suppose to assume that the function is continuous, which would make my picture invalid.

As you can see from the picture though, the limit can exist while the function is defined elsewhere (if it's not continuous).

So hmmm :)