How do you find a removable discontinuity for a function?

1 Answer
Jul 26, 2014

A discontinuity #a# of a function #f# is removable if #lim_{x to a} f(x)# exists (that is, is a finite number). If the limit fails to exist (for instance, if it is infinite, or there are different one-sided limits, etc), the discontinuity is non-removable.
Thus, to decide if a discontinuity #a# of a function #f# is removable, you need to examine #lim_{x to a} f(x)#.
See this video on "finding discontinuities" for details.