Replies:
L'Hopital's rule is one of several forms of the Mean Value Theorem of
differential calculus. You can find it discussed in most all first year
Calculus texts (although in looking him up, there is some disagreement as to
the spelling of his name??).
The rule has several conditions of continuity which makes it difficult to
write down in a very concise manner, given the format of this forum. But
assuming the functions
f(x), g(x) and their derivatives f'(x), g'(x) are "well behaved" the theorem
states:
lim x-->xo [f(x)/g(x)] = lim x-->xo [f'(x)/g'(x)]. In words: the ratio of
the functions f(x) and g(x) and the ratio of their respective derivatives is
the same as x-->xo.
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