Question

In the following, we will tse a kmown power series to approximate 1/2 arctan(r) dr to within 0.00001 of the actual value of the definite integral (a) [2pt] Use a known power series representation to express (ctan(x) as a Maclaurin series. What is the radius of the series convergence? 1/2 (b) [4pts] Use your answer from part (a) to express(r) dr as an alternating series (c) [6pts] Your series in part (b) will converge by the Alternating Series Test. (You do not have to show this.) Approximate the alternating series you found in part (b) (and hence the definite integral) to within 0.00001 of the actual value by using as many terms as needed. Be sure to justify why the nunber of ternm that you have used is enough!

Answer 1

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