In a Taylor polynomial, how would I find the upper bound for the error of the approximation: arctan(0.4) = 0.4 - (0.4)^3/3! . Thanks

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- Feb 26th 2006, 04:15 PMme > jallison + brownieTaylor Theorum
In a Taylor polynomial, how would I find the upper bound for the error of the approximation: arctan(0.4) = 0.4 - (0.4)^3/3! . Thanks

- Feb 26th 2006, 10:53 PMCaptainBlackQuote:

Originally Posted by**me > jallison + brownie**

alternating series (the sign of consecutive terms is alternately + and -) of

decreasing terms so the absolute error is less than the absolute value first

ignored term. In this case the Taylor series is (as we are interested in

):

(note you have an error in your Taylor polynomial).

So in this case if we truncate after the second term the absolute error in the

approximation is less than:

RonL