It is usually possible to apply arithmetic operations to manipulate limits like the following:

However, there are certain combinations of particular limiting values cannot be computed in this way. We say that those limits are in an indeterminate form, informally described by one of the following: 1

Solving Indeterminate Forms

If we can perform algebraic manipulation to make a limit the form of or , then we can use L’Hospital’s rule.

We can also use well known result such as the sinc function limit , which itself can be proved by the squeeze theorem.

Solve

Note that we have the indeterminate form .

Also, note that even though we get from this limits, not all limits in the form has one as a result.

Footnotes

  1. Indeterminate form - Wikipedia