Is h continuous on the interval (2,5)?
There are no points in (2,5) where h is undefined, so we don't need to worry about that. The only point in (2,5) where the limit might be disagreeable or not exist is at x = 4.The left-hand limit is
The right-hand limit is
Since the one-sided limits disagree, doesn't exist, therefore h is discontinuous at x = 4. Therefore h is not continuous on the interval (2,5).