## L'Hospital's Rule

Let lim stand for the Limit , , , , or , and suppose that lim and lim are both Zero or are both . If

has a finite value or if the Limit is , then

L'Hospital's rule occasionally fails to yield useful results, as in the case of the function . Repeatedly applying the rule in this case gives expressions which oscillate and never converge,

(The actual Limit is 1.)

References

Abramowitz, M. and Stegun, C. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, p. 13, 1972.

L'Hospital, G. de L'analyse des infiniment petits pour l'intelligence des lignes courbes. 1696.