411 REFERENCE · Wikibooks
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