Check the picture below.
now, when it comes to limits, we're not concerned if the value of the function is the same as the limit at that location, we're only concerned on to where is the function approaching, now it may not get there, but that is where it's approaching or seem to be approaching.
in this case, the piece-wise function has a hole when x = 3, meaning f(x) ≠ 3 when x = 3, however if we look at the progress from say 6, 5.9, 5.5, 5.1, 4.9, 4.8, 4.1, 3.7, 3.000001, it seems to be approaching 3, thus that is its limit.