(a Use the series for arctan(x) to write the first four nonzero terms and the general term of the Maclaurin series for f. (b) The radius of convergence of the Maclaurin series for f is 1. Determine the interval of convergence. Show the work that leads to your answer. (c) Write the first four nonzero terms of the Maclaurin series for f'(2t).
(a Use the series for arctan(x) to write the first four nonzero terms and the general term of the Maclaurin series for f. (b) The radius of convergence of the Maclaurin series for f is 1. Determine the interval of convergence. Show the work that leads to your answer. (c) Write the first four nonzero terms of the Maclaurin series for f'(2t).
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please answer all parts since it is one question and for the first part please leave the terms in factorial form
![Let f(x) = arctan(x*)
(a) Use the series for arctan(x) to write the first four nonzero terms and the general term of the Maclaurin
series for f.
(b) The radius of convergence of the Maclaurin series for f is 1. Determine the interval of convergence. Show
the work that leads to your answer.
(c) Write the first four nonzero terms of the Maclaurin series for f'(2t).
(d) If g(x) = 6 f'(2t)dt, use the first two nonzero terms of the Maclaurin series for g to approximate g ().
%3D
(e) The Maclaurin series for g. evaluated at x = 1, is a convergent alternating series with individual terms that
decrease in absolute value to 0. Show that your approximation in part (d) must differ from gE) by less
than 0.1.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4143f45a-5c96-4449-af2f-abda697f3e91%2Fc4a8cf33-6d79-4bf9-ad4a-ad1469f6127f%2Fyjyzis_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let f(x) = arctan(x*)
(a) Use the series for arctan(x) to write the first four nonzero terms and the general term of the Maclaurin
series for f.
(b) The radius of convergence of the Maclaurin series for f is 1. Determine the interval of convergence. Show
the work that leads to your answer.
(c) Write the first four nonzero terms of the Maclaurin series for f'(2t).
(d) If g(x) = 6 f'(2t)dt, use the first two nonzero terms of the Maclaurin series for g to approximate g ().
%3D
(e) The Maclaurin series for g. evaluated at x = 1, is a convergent alternating series with individual terms that
decrease in absolute value to 0. Show that your approximation in part (d) must differ from gE) by less
than 0.1.
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