I've built a worksheet that I'll use next week to motivate the idea of
polynomials approximating more complicated functions.  It is very fast-
and-loose with the mathematics because I want it to precede our study
of infinite series, so any serious tests of convergence are covered by
vigorous hand-waving.

I've posted this here as another in my series of experiments creating
interactive texts with Sage.  This was authored in LaTeX with the
eventual worksheet as the end-product.  I've produced a PDF from the
same source to handout to the students, but of course it won't have
the interactivity.  If you view the worksheet, there's a bit of
screwiness with some of the displayed math (the arctan stuff) which is
a result of avoiding a more serious bug in TeX4ht (which should be
fixed eventually).  This creation still requires one small conversion
step with a custom script I wrote.  Eventually this step could be
eliminated.

Caveats:  It contains four @interact demonstrations so you can't run
it off of sagenb.org and must instead download it from the URL below
to run/view locally and get the full effect, or else its liable to
look pretty crummy - no interact's and perhaps the jsMath won't get
rendered right.  It also seems the horizontal axes are expanded when
they are first run, so to get the intended plots, try re-evaluating
each demonstration.  I had a screenshot, but my email attempts to post
it keep failing.

http://sagenb.org/pub/383/

Rob
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