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




Re: This integral is a doozii....
Posted:
Oct 15, 2001 9:33 AM


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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