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L'Hôpital's rule

You can calculate the limit of a quotient using L'Hôpital's rule

if the function in this point is indefinite.



You may even repeat this rule several times to get a useful result. You may use l'Hôpital's rule only if it is necessary to get a correct result. This sounds rather strange, but in practice it works well.


Example 1

A simple limit is



Example 2

A simple limit is



Example 3

A logarithm is a limit because


Example 4

A limit with the sinc function is



Example 5

A limit with the cosine is



Example 6

A limit with the sine can be solved directly

If you use l'Hôpital's rule here it goes wrong, because


and that is not correct.


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