# Famous Theorems of Mathematics/L'Hôpital's rule

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Consider some limit

which cannot be evaluated directly, that is, either f(a) = g(a) = 0 or

L'Hopital's rule says that

Suppose both are equal to zero. The Newton definition of the derivative is

Therefore,

Now suppose that both and diverge to positive or negative infinity. Another way to define the derivative is by

Then

QED