Question

If f(2)=4, can you conclude anything about the limit of f(x) as x approaches 2? Explain your reasoning.

Answer 1

Let's consider an example:
\[f(x)=\begin{cases}4&\text{for }x\le2\\
1&\text{for }x>2\end{cases}\]

Can you say anything about the limit?

Answer 2

i can say that it does not have a limit due to the jump. Not sure if thats correct.

Answer 3

Right, the limit doesn't exist, even though the function is defined at \(x=2\).

So just because the function is defined at a given point doesn't mean the (two-sided) limit exists.

Answer 4

thanks so much :)

Answer 5

You're welcome