The series representing the integral1/3 In (x+ 1)dr is given byO A.(-1)"+1n=1 3" (n+ 1) 2O B. None of the choices in the list.C.(-1)"+1n=0 3" +1(n+1) 2O D.00Σ(-1)"+1n=0 3" (n+1) 2OE.(-1)"+1n=13" n2

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Answered: 1/3 In (x+1) The series representing…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

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Problem 1RQ

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Use the following information to complete parts a. and b. below. f(x) = 13 Inx, a = 4 a. Find the first four nonzero terms of the Taylor series for the given function centered at a. 13 O A. The first four nonzero terms are 13 In 4+ 13 13 4(x-4)- -(x-4) + (x-4)³. 32 192 13 O B. The first four nonzero terms are 13 In 4-- 13 13 4 (x-4)- -(x-4)². 16 32 (x-4)³ 13 13 O C. The first four nonzero terms are 13 2 (x-4). (x-4)² + 4 32 -(x-4)³. 192 13 13 O D. The first four nonzero terms are 13 4 32 (x-4). 32 (x-4)²+. b. Write the power series using summation notation. 13(-1)+1(x-4) Ο A. 13In 4+ Σ 4k k=1 OB. 13 In 4+ (-1). k=0 13(-1)k+1 O C. 13 In 4+ k=0 4²(x-4) k OD. 13 In 4+ (−1)k+1.. =(x-4) k 13 k.4k k=1 13 4*(x-4)k + + 13 1024 64(x-4)³ 39 2
Evaluate L{e* (r +r* -1)}. calth of 6. 2. A. (s –2)* (s-2) (s – 2) NTS TO- 6. 21 В. (s+2)* (s+2) (s+ 2)* ey C. (s-2) (s-2) (s–2)* D. 4 ) (s-4)* S-4 1 E. s+4 (s+4) (s +4) * 1. 1. 3.
Find the Fourier series for the function f (x) shown below. Towards which values does this series converge for x = 0, ½, -1, 1, 4, 9?
Use the following information to complete parts a. and b. below. f(x) = 11 Inx, a = 5 a. Find the first four nonzero terms of the Taylor series for the given function centered at a. OA. The first four nonzero terms are B. The first four nonzero terms are ∞ Ο A. 11 In 5+ Σ (-1)* - k=0 8 11 OC. The first four nonzero terms are 11 In 5+ 5 D. The first four nonzero terms are 11 In 5- OB. 11 In 5+ (−1)k+1. k=1 11 5*(x-5)k 8 Ο c. 11In 5+ Σ k=1 11 5 11 11 5 b. Write the power series using summation notation. k.5k + -(x - 5)k 11(-1)+1(x-5)k 5k 11 50 (x-5)- 11 + (x-5)- 50 11 5 22 125 -(x-5)- 11 375 11 (x - 5)² + 50 (x - 5)² + ¯(x − 5)² + 33 125 11 2500 11 375 (x - 5)³. 125 ¯(x – 5)³. -(x - 5)³. (x - 5)-(x - 5)²-(x - 5)³.
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b. . b. Find the Fourier sine series expansion of the function f(x) = x² +M, 0S×S M. (Note: M is a number in your ID number after the letter For S and M>0) M=1
for 0 < 0 < 27. The foregoing result is known as Lagrange's identity and is useful in the theory of Fourier series. 50. Suppose z1, 2, 23, and z4 are four distinct complex nunbers. Interpret gec- metrically: 21 2 arg 23 |3D 24
Attached.
3. * x-1/3 dx = 00, so the series diverges.
H.w: Find the Fourier series for the following functions: and The function is odd or even? -T≤x≤0 0≤x≤ π 1-f(x) = 2x x

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1/3 In (x+1) The series representing the integral dr is given by O A. (-1)"+1 n=1 3" (n+ 1) 2 O B. None of the choices in the list. C. Σ (-1)"+1 n=0 3" +' (n+ 1) 2 Σ n=0 3" (n+ 1) 2 OD. (-1)"+1 O E. (-1)"+1 Σ n=1 3" n2