How do I know if a discontinuity in a function is removable or not?

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Answer 1 · 2018-04-16T18:03:18

If the limit exists, it is removable. Otherwise, not.

If #f# is discontinuous at #a#,

then #lim_(xrarra)f(x) != f(a)#

This could be for any of 3 reasons:

#lim_(xrarra)f(x)# fails to exist

#f(a)# fails to exist

Both exist, but they are unequal.

If the limit exists, the discontinuity is removable.