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Question:
WHAT IS THE EQUATION OF L'HOPITAL RULE?



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.

Vince Calder



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