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

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) (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

(which could be a consequence of the non-existence of the limit).

John

My calculator said it, I believe it, that settles it

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