Question

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

Answer 1

Here's an example:
\[f(x)=\begin{cases}2x&\text{for }x\not=2\\1&\text{for }x=2\end{cases}\]

Answer 2

so i can conclude that there is a hole? that is what i originally thought, but i wanted to double check

Answer 3

Not necessarily. If you were given \(f(x)=2x\) for all \(x\), then the limit as \(x\to2\) is 4 and \(f(2)=4\).

For the example I gave, though, the limit exists, but \(f(2)\) need not be equal to 4.

Answer 4

alrighty thanks :)