SOLUTION: what does it mean to be continuous at x=1, as well as what it means to have discontinuity at x=1.

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Question 624103: what does it mean to be continuous at x=1, as well as what it means to have discontinuity at x=1.
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Let be a point in the domain of the function . Then is continuous at if and only if:



So, the statement that is continuous at means two things. 1: The value is an element of the domain set of and 2: . The existence of the limit being implied by the fact that it equals something.

The statement that is discontinuous at means that either the value is not in the domain set of or (which could be a consequence of the non-existence of the limit).

John

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