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Choose from the following each TRUE statement. OA. The Taylor series representation for flx) = e3x centered at a = 1 is E 3 e3 -(x- 1)" with radius of convergence R= n=0 n! O B.

Choose from the following each TRUE statement. OA. The Taylor series representation for flx) = e3x centered at a = 1 is E 3 e3 -(x- 1)" with radius of convergence R= n=0 n! O B.

Advanced Engineering Mathematics
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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Choose from the following each TRUE statement. OA. The Taylor series representation for f(x) = e3x centered at a =1 is > 3"e3 (x – 1)" with radius of convergence R= 00 n=0 n! OB. The integral x2sin(x)dx (-1)" n=0 (2n+ 1)!(2n+4) can be evaluated with and infinite series to be c 5 y2n +4 for the radius of convergence R= co . UC The Maclaurin series representation for f(x) = arctan(x²) is2 (-1)" 4n+2 with radius of convergence R= 1 n=0 (2n+ 1)! OD. The integral can be evaluated with and infinite series to be c E yn +2 for the radius of convergence R = 1. 1- x n=0 OE. (- 1)" Σ (2n)! The Maclaurin series representation for f(x) = cos(x²) is 4n with radius of convergence R= 00 n=0 D- The Taylor series representation for fx) = sin(x?) centered at a = I is (– 1)" y2n+1 with radius of convergence R= 00 n=o (2n+ 1)!
Transcribed Image Text:Choose from the following each TRUE statement. OA. The Taylor series representation for f(x) = e3x centered at a =1 is > 3"e3 (x – 1)" with radius of convergence R= 00 n=0 n! OB. The integral x2sin(x)dx (-1)" n=0 (2n+ 1)!(2n+4) can be evaluated with and infinite series to be c 5 y2n +4 for the radius of convergence R= co . UC The Maclaurin series representation for f(x) = arctan(x²) is2 (-1)" 4n+2 with radius of convergence R= 1 n=0 (2n+ 1)! OD. The integral can be evaluated with and infinite series to be c E yn +2 for the radius of convergence R = 1. 1- x n=0 OE. (- 1)" Σ (2n)! The Maclaurin series representation for f(x) = cos(x²) is 4n with radius of convergence R= 00 n=0 D- The Taylor series representation for fx) = sin(x?) centered at a = I is (– 1)" y2n+1 with radius of convergence R= 00 n=o (2n+ 1)!
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