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An elementary, limit-free calculus for polynomials

Published online by Cambridge University Press:  23 January 2015

Alasdair McAndrew
Alasdair McAndrew*
Affiliation:
Victoria University, PO Box 14428, Melbourne, Victoria 8001, Australia, e-mail:Alasdair.McAndrew@vu.edu.au
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Extract

This work grew out of a simple problem: how could I introduce the basic concepts of calculus to students who were mathematically under-prepared? It has been pointed out by many authors (see [1] and its references) that limits are a major stumbling block for many students beginning their study of calculus. Part of the difficulty with limits is the conceptual confusion between process and value. Some limits can be evaluated by a simple process of substitution, for example,

while others cannot, for example,

Type
Articles
Information
The Mathematical Gazette , Volume 94 , Issue 529 , March 2010 , pp. 67 - 83
Copyright
Copyright © The Mathematical Association 2010

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References

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