Andrew F. answered • 11/25/21

Experienced private school teacher

Meesam, this is a great and deep question with no quick full answer. Remember that limit as x approaches 3 means x can not be 3. Therefore lim x—> 3 (x - 3)/(x - 3) is one, is not undefined. We say a limit exists or a limit does not exist, but we do not say “ undefined “—that is for things that have no definition, such as division by zero. An example of a limit which does not exist is when the value gets larger than any positive number when we approach 3 from one side, but smaller than any negative number when we approach 3 from the other side—(1/(x - 3)) is an example. Hope this helps a little—Andrew

Dayv O.

11/26/21

Andrew F.

Dayv O. I find it more helpful to say limits exist or do not exist-- I would say the limit of 1/x exists for all non- zero numbers. If you prefer to say that when the value of a limit does not exist, then the limit is undefined, I do not object. I worry that this might create confusion-- can you say why you prefer to stress undefined?11/26/21

Dayv O.

11/26/21

Meesam T.

Thanks for your answer.Well that does make more sense.11/26/21