Available online
Description
This programme takes a geometrical look at L'Hopital's rule.
This programme takes a geometrical look at L'Hopital's rule.
| Module code and title: | M203, Introduction to pure mathematics |
|---|---|
| Item code: | M203; 01B; 1995 |
| First transmission date: | 16-08-1987 |
| Published: | 1995 |
| Rights Statement: | |
| Restrictions on use: | |
| Duration: | 00:24:29 |
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| Producer: | Michael Peet |
| Contributors: | David Brannan; Roy Nelson |
| Publisher: | BBC Open University |
| Keyword(s): | Cauchy Mean Value Theorem; Marquis Guillaume de L'Hopital; Mean Value Theorem; Parametric plan; Right/left limit; Rolle's Theorem |
| Subject terms: | Geometry |
| Footage description: | If you have two continuous functions f(x) and g(x) which are both zero at the same point c, what can you say about the ratio f(x) / g(x) as x tends to c? Two different problems of this kind are solved during the programme by applying L'Hopital's Rule, which says that the ratio equals f (x) / g'(x), under certain circumstances, but first that Rule is derived from first principles. Roy revises Rolle's Theorem in order to use it in a geometrical proof of the Mean Value Theorem. David then demonstrates the Cauchy Mean Value Theorem, which gives a version of the Mean Value Theorem for curves given in parametric form. Roy considers the special case where the parametric curve passes through the origin to prove L'Hopital's Rule. Before summarising David proceeds to solve the first problem before going over the steps which lead to the proof of the Rule. The programme ends by looking at different ways of interpreting L'Hopital's Rule: David examines what the Rule says geometrically, with graphs of the functions in Problem 1. Roy "steps back in time" and, dressed in 17th Century costume, explains how L'Hopital derived his result. Finally, David applies the Rule twice in order to solve the second problem raised in the programme. |
| Master spool number: | DOU8125 |
| Production number: | FOUM492N |
| Videofinder number: | 2277 |
| Available to public: | no |
