Which discontinuities are removable?
In this video we talk about the different kinds of discontinuities and show which discontinuities are removable and which are nonremovable.
As it turns out, only point discontinuities are removable, which is why point discontinuities are often called removable discontinuities. Jump and infinite discontinuities are not removable, because we can’t easily patch the holes in their graphs.
But we can easily patch a point discontinuity, just by redefining the function at that point. This will “fill” the hole in the graph, removing the discontinuity and making the function continuous.