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Chords, tangents and the Leibniz notation

By David Tall

Abstract

In this article I continue my quest for “understanding the calculus” 1,2 by looking at a practical approach to the notion of a tangent and linking it to the Leibniz notation\ud dy/dx in a meaningful way. The latter is a bête noire for students: it looks like a quotient, it acts like a quotient, yet the seeds of a classic psychological conflict are sown in their minds when they are told it must not be thought of as a quotient. I shall discuss how this conflict may be resolved so that the chain law allows cancellation

Topics: QA
Publisher: Association of Teachers of Mathematics
OAI identifier: oai:wrap.warwick.ac.uk:497

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Citations

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