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LHospitals Rule Tiffany Hall and Amanda Boggs

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LHospital Born in Paris in 1661 Was a cavalry officer until his nearsightedness forced his resignation After he resigned, he studied math under Johann Bernoulli

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LHospital and Bernoulli LHospital agreed to support Bernoullis works if he would publish LHospitals book LHospitals book, Analyse des infiniment petits pour l'intelligence des lignes courbes, contained LHospitals Rule There was a dispute as to whose ideas were used in the book. LHospital claimed they were his own, but Bernoulli stated that they were his. Letters written between the two mathematicians were found in 1955 which proved that Bernoullis claims were correct. Johann Bernoulli

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LHospitals Rule =0 = = and Suppose that f and g are differentiable and g(x) 0 on an open interval I that contains a (except possibly at a). Suppose that: or that Then: = if the limit on the right side exists (or is + or - ) (according to Stewart Calculus 3 rd Edition)

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Indeterminate Forms

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How to Apply the Rule If its in a fractional form, take the derivative of the top and the derivative of the bottom. Then take the limit. Repeat this process until the answer is not in an indeterminate form.

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Example w/ the Fractional Form = = 1

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Proof Look at the linear approximation to f(x) and g(x) at x=a When x is close to a, the the ratio is: This ratio approaches f(a)/g(a) as x a is g(a) 0

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Works Cited Stewart, James. Calculus. 3 rd ed. Pacific Grove, CA: Brooks/Cole Publishing Company, 1995. http://www.geocities.com/mathladies/bios/johannb.html http://www-groups.dcs.st- and.ac.uk/~history/Mathematicians/De_L'Hopital.html http://www-groups.dcs.st- and.ac.uk/~history/Mathematicians/De_L'Hopital.html http://www-math.mit.edu/~djk/18_01/chapter26/proof01.html

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