To approximate using a Taylor polynomial, we coulduse the series for the arctangent or
Chapter 10, Problem 23(choose chapter or problem)
To approximate using a Taylor polynomial, we coulduse the series for the arctangent or the series for the arcsine.In this problem, we compare the two methods.(a) Using the fact that d(arctan x)/dx = 1/(1 + x2)and arctan 1 = /4, approximate the value of usingthe third-degree Taylor polynomial of 4 arctan xabout x = 0.(b) Using the fact that d(arcsin x)/dx = 1/1 x2and arcsin 1 = /2, approximate the value of usingthe third-degree Taylor polynomial of 2 arcsin xabout x = 0.(c) Estimate the maximum error of the approximationyou found in part (a).(d) Explain the problem in estimating the error in thearcsine approximation.
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