Electronic Proceedings of the Seventh Annual International Conference on Technology in Collegiate MathematicsOrlando, Florida, November 17-20, 1994Paper C010Finding Derivatives Without the Notion of Limits |
D. Reginald TraylorIncarnate Word College 4301 Broadway San Antonio, TX 78209 USA Phone: (210) 829-6003 Fax: (210) 829-3922 list of all papers by this author | Julia S. RomanIncarnate Word College 4301 Broadway San Antonio, TX 78209 USA Phone: (210) 829-6003 Fax: (210) 829-3922 jlroman@tenet.edu list of all papers by this author |
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ABSTRACT
This paper extends the work of Julie Roman and announces a remarkably simple, but rigorous, method with which to find derivatives of the entire class of rational functions without the notion of a 'limit.' Based on R.L. Moore's definition of slope of a simple graph, this innovative method of determining the derivative of a function is reduced to finding the slope of a simple graph and calls upon no greater mathematical sophistication than that of high school algebra. That is, most of the material normally taught in a first year calculus course can be taught without the complication of the concept of a limit, making the treatment considerably more palatable to the student.It is expected that this approach to derivatives will provide a basis for three textbooks. Under development now is a text for Business Mathematics. These methods have been used for three semesters in that course. Also planned are texts to satisfy the requirements for a liberal arts major and a high school calculus text.
The graphing calculator and Power Point software are used throughout the teaching effort and presentation of these research results.
Keyword(s): calculus, graphing calculators, derivatives