Question #f7807

1 Answer
Jim H
Feb 14, 2017

See below.

Explanation:

In terms of the definition of "continuous at #a#"

If #f# is discontinuous at #a#

but #lim_(xrarra)f(x)# exists, then the discontinuity is removable,

and if #lim_(xrarra)f(x)# fails to exist, then the discontinuity is non-removable,

In terms of the graph:

A removable discontinuity occurs if the is a hole in the graph at #a#, but it is clear how to fill in the hole.

A non-removable discontinuity occurs if there is a jump (finite or infinite) or if the limit fails to exist for any other reason.
("Other" reasons include #sin(1/x)# at #0#.)

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