arctan(x) ) Find the MacLaurin series for

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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Pls help pls pls pls pls pls pls pls pls. Pls do all the parts. 

arctan(x)
4. (a) Find the MacLaurin series for
1
[Note: arctan is sometimes written tan-1. Use the fact that arctan(x) =
1+x
d
dx
(b) Assuming that this series satisfies the hypotheses of the alternating series estimation theorem
(terms decrease in absolute value and approach zero), use this theorem to obtain an estimate for
0.4
arctan(x) dx to within 10-s.
5 decimal digits.
Transcribed Image Text:arctan(x) 4. (a) Find the MacLaurin series for 1 [Note: arctan is sometimes written tan-1. Use the fact that arctan(x) = 1+x d dx (b) Assuming that this series satisfies the hypotheses of the alternating series estimation theorem (terms decrease in absolute value and approach zero), use this theorem to obtain an estimate for 0.4 arctan(x) dx to within 10-s. 5 decimal digits.
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