Indeterminate form: Difference between revisions

Revision as of 07:01, 7 September 2004

Revision as of 07:05, 7 September 2004

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==Logical circularity==

In some cases it may constitute [[circular reasoning]] to use L'Hopital's rule to evaluate such limits as

:<math>\lim_{h\to 0}{(x+h)^n-x^n \over h}.</math>

If one uses the evaluation of the limit above for the purpose of ''proving'' that

:(''d''/''dx'') ''x''^''n'' = ''nx''^{''n''&minus;1}

and one uses L'Hopital's rule and the fact that

:(''d''/''dx'') ''x''^''n'' = ''nx''^{''n''&minus;1}

in the evaluation of the limit, then one's reasoning is circular and therefore fallacious.