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The first line should be <math>g'(x) \not\equiv 0</math> not <math>g'(x) \ne 0</math>, since it can still be 0 at some places. [[User:ChuckK|ChuckK]] 08:53, 23 June 2009 (EDT)
The first line should be <math>g'(x) \not\equiv 0</math> not <math>g'(x) \ne 0</math>, since it can still be 0 at some places. [[User:ChuckK|ChuckK]] 08:53, 23 June 2009 (EDT)
:You're right, of course -- indeed this is the case in the second example given. The statement of the theorem right now isn't entirely precise, and it should also mention that the limit <math>f'(x)/g'(x)</math> must exist. There are cases in which f/g is indeterminate, and the limit of f/g exists, but the limit of f'/g' does not exist. I'd make these edits, but the page seems to be locked now... --[[User:MarkGall|MarkGall]] 11:07, 23 June 2009 (EDT)