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The Calculus as an Item in School Mathematics

Published online by Cambridge University Press:  03 November 2016

C. S. Jackson
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Extract

A bold induction by simple enumeration has been made. The graph when plotted confirms it. Let elementary algebra justify it. A little later the algebra will come first.

Just when to introduce the synlbol Δ is of course a question of knowing the class.

How the differences give the slope of certain chords will be evident. How far at this stage to allow the question of the tangent to arise is a question of tact.

Type
Research Article
Information
The Mathematical Gazette , Volume 7 , Issue 109 , January 1914 , pp. 243 - 246
Copyright
Copyright © The Mathematical Association 1914

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References

* Of course a simpler example would be given to the schoolboy to begin with—perhaps y=x2-x. The example in the text is intended to show how what would be a somewhat tedious and troublesome graph may be rapidly plotted without algebraic transformation. There is no necessity to complete the y column. All plotting may be done by means of Δy.