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This topic is most easily handled using an aplet from
The HP HOME View web site (at
http://www.hphomeview.com). This aplet, called "Curve
Areas" will draw rectangles either over or under a curve
or use trapezoids. A number of curves are supplied pre-
set but the user can also enter their own. The user can
nominate the interval width and the number of
rectangles.
Most importantly, a worksheet is bundled with the aplet which will lead the
student through the process of deducing an area function and hence to the
anti-differentiation of
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One of the concepts which students find quite difficult to come to grips with is
that of sketching a field of slopes from a derivative function and, from this,
sketching a family of curves. An aplet from The HP HOME View web site (at
http://www.hphomeview.com), called "Slope Fields", will assist with this
process.
In this aplet the user enters the derivative function into F1(X) and then uses
the VIEWS menu to produce a field of slopes. A cross-hair is
projected onto the field which the user can move around.
When the user presses ENTER, a curve is drawn, starting at
that point and projecting to the right and then the left, and
following the field of slopes. Repetition of this will illustrate the fact that there
are a family of curves, separated by a constant, which all fit the 'description'
of the function stored in F1(X).
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