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L'Hôpital's theorem

The limit of a quotient can be calculated with l'Hôpital's rule

if the function in this point is indeterminate.



We start from the function

of which we have determined that at the point a this function is indeterminate. Then you can try to approximate this point as a limit, so

This can be written in simplified form as

Now we play with the differentials du and dv, then we get

This seems like hocus pocus, but it immediately follows l'Hôpital's rule



The name of this theorem is a tribute to the French mathematician Guillaume de l'Hôpital (1661 - 1704).

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