Question

The Maclaurin series for sin(x) is x + - + ... 3! 5! 7! sin You need not write your answer in summation notation, but you do need to list at least 4 nonzero terms. b) Find the Maclaurin series for xsin(x). You need not write your answer in summation notation, but you do need to list at least 4 nonzero terms. c) Use the first four terms of the appropriate power series to approximate V2 2

Answer 1

27 - + 7! The MacLaurin series for sina is 75 not one Replacing a with And we get the Maclaurin series for Sin lum). Sin (4.a) Thus, the Maelaurin series for sin ( 1 ) is x - (n) (n)? + 3! 5! 575 25 7! 17 4771 73 11 + • n 23 + 43.3? 45.5! by multiplying n get Maclaurin series of asinn with maclaurin series of sinx. This Maclaurin series of nsinn is 73 3! an² n4 a(n. me as n 71 1 . + 28 71 From @ Sin (**) = fm met my as for n=l, 45.51 s 77 21+ 47.7! 87 t Sin (14) = 1 14 75 45.51 PRETO itt 03 4231 n 43.31 dz 2 =7 c 75 n7 t tinn 45.51 47.7! 0:707106