Quality of Approximation by Geometric Series

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This Demonstration shows graphically and numerically the quality of approximating the function values of for any by the Taylor polynomial , where .

Contributed by: Reinhard Simonovits (September 2012)
With additional contributions by: Bernd Thaller
Open content licensed under CC BY-NC-SA

Snapshots

Review questions:

Let and . How large is the error?

Let . For what is the error less than 0.01?

Let and . How large is the error?

Let . Check the error for . (The point is the "best" point since it is the expansion point.)

For , at which is the error largest?

For and , how large is the error?


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