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Topic: This integral is a doozii....
Replies: 14   Last Post: Oct 17, 2001 12:07 AM

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Terence Gaffney

Posts: 45
Registered: 12/6/04
Re: This integral is a doozii....
Posted: Oct 15, 2001 9:33 AM
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sin(x)/x is a wonderful example of a difficult problem becoming simple
with the right viewpoint. The place to really work on it in the
curriculum is during the study of power series.There you can easily see
why derivatives of all orders of sin(x)/x exist at the origin. At this
point you can show the students that the behavior of a rational function
at complex points affectsthe radius of convergence, building a foundation
for treating the improper integral through residues at some point in the
future.

To build up to the power series punch line you can look at the graph of
sin(x)/x when you discuss the derivative of sin(x), and discuss the
numerical computation of definite integrals involving this function during
the discussion of numerical integration.

Best,
Terry Gaffney




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