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L'Hôpital's rule for 0/0

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

if the function gives 0 / 0 or ∞ / ∞ in that point.

 


Explanation

In the point x = a you then get f (a) = 0 and g (a) = 0, so the slope of the tangent lines for these functions is

The functions and the tangent lines come together in this point, and substitution of m (x − a) gives then

so that

 


History

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


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