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Description
In this programme a new definition of the scale factor is arrived at and used to give a derived function. A computer animation sequence shows how a derived function is plotted on a graph.
Module code and title: M101, Mathematics: a foundation course M101; 11 07-05-1978 1978 00:24:22 + Show more... Jean Nunn Graham Read; Colin Rourke; Allan I.,1936-2013 Solomon BBC Open University Calculus; Converge; Differentiation; Scale factors; Slope; Tangent; Trigonometry; Chord From Block II of the course the students have learnt how the scale factor at a point controls or expands errors under a given function. But working out scale factors for some functions such as sin x,is a problem. In this programme, the first in the Calculus Block, Allan Solomon and Colin Rourke show how the definition of the scale factor, together with the idea of the limit of a sequence of values can be used to define the derivative at a point of a function. This derivative can be interpreted as the slope of the tangent at that point to the curve of the function. What happens if you look at the derivatives at every point of a curve? Allan Solomon and Graham Read demonstrate how this produces the derived function and show, with computer animations, the generation of derived functions for some familiar curves (including sin x). In the post programme work students are lead through the formal definitions involved to the algebraic techniques of differentiation. 6HT/72486 00525_4248 2464 no