Look at the form of the remainder of the truncated Taylor series. This is anOriginally 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: