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, 03:15 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, 09:53 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

$\displaystyle |x|<1$):

$\displaystyle

\arctan(x)=x-\frac{x^3}{3}+\frac{x^5}{5}-...

$

(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:

$\displaystyle

\left| \frac{x^5}{5} \right|=\frac{(0.4)^5}{5}\approx 0.002

$

RonL