Use a taylor polynomial to approximate at x=0.1 with error less than 0.001.

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- Aug 8th 2009, 01:47 AMroshanheroTaylor polynomial
Use a taylor polynomial to approximate at x=0.1 with error less than 0.001.

- Aug 8th 2009, 02:58 AMFailure
The n-th derivative of f is . If you develop f around you get

Where . To make the error term for smaller than 0.001, we solve the following (worst case) inequality for n

which gives, if I'm not mistaken, that . Thus we take and get:

. Compare this with the exact value of : the resulting error is less than 0.001, as required.