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17Calculus - Limits That Do Not Exist

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Difference Between A Limit Going To ±Infinity and A Limit That Doesn't Exist

Topics You Need To Understand For This Page

One-Sided Limits

Many people get confused between the case when a limit goes to infinity (or negative infinity) and when a limit does not exist. And there is a good reason for the confusion. Many discussions I've read do not separate the two cases. But they are different.

When a Limit DOES Exist

When a limit goes to positive or negative infinity, the limit DOES exist. The limit is exactly that, positive or negative infinity.

When a Limit DOES NOT Exist

There is only one case when a limit doesn't exist: when the limit is different from the left than it is from the right. This concept requires understanding one-sided limits. There are videos on that page showing examples of when the limit doesn't exist.

For more detail including graphs, see the substitution section on the finite limits page. And, as usual, check with your instructor to see how they define limits that do not exist.

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