Simple question, I just cannot find something that explains it right out and to the point without giving a huge confusing explanation. The question that I am struggling with is to determine a limit of a function if it exists.
Find: $\lim_{x\to2}{f(x)},$
If
$f(x)=\begin{cases}x^{2} & \text{if } x<2 \\ 3 & \text{if } x=2 \\ 3x-2 & \text{if } x>2\end{cases}$
Now i worked out the limits from both sides and they both equal 4. But it does say that the limit at that point equals 3. Does this mean that the limit doesn't exist? Or does this just mean that the double sided limit exists at 4, but is discontinuous and equals 3 at that point?
Thanks in advance!