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Looking at graphs through infinitesimal microscopes, windows and telescopes

Published online by Cambridge University Press:  22 September 2016

David Tall
David Tall*
Affiliation:
Mathematics Education Research Centre, University of Warwick, Coventry CV4 7AL
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Extract

The differential triangle of Leibniz for a real function f is found by taking an increment dx in the variable x, finding the corresponding increment dy in y = f(x) and drawing the ‘triangle’ in Fig. 1. Here ds is the increment in the length of the graph, where

and the derivative of f is

Type
Research Article
Information
The Mathematical Gazette , Volume 64 , Issue 427 , March 1980 , pp. 22 - 49
Copyright
Copyright © Mathematical Association 1980

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References

1. Robinson, A., Non-standard analysis. North-Holland (1970).Google Scholar
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