Quality of Approximation by Geometric Series

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

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DETAILS

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?
For and , how large is the error?
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