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he origin for the function 5+2 sin(x²). : -1 | |-100 | 13 : -2 = 2

he origin for the function 5+2 sin(x²). : -1 | |-100 | 13 : -2 = 2

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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(part 1 of 4) Find the coefficient of 6 in the Taylor series expansion centered at the origin for the function f(x) = 6+2 sin(x²). 1. coefficient 2. coefficient ofx6 3. 4. 5. coefficient ofx6 = 2 on (-∞, ∞). = 1 coefficient ofx6 = 3 coefficient ofx6 (part 2 of 4) Find a power series representation for the function f(x) = x sin(2x) 1. f(x) = Σ (−1)n-1. n=1 5. f(x) ∞ 2. f(x) = Σ (-1)″-1. n=1 6. f(x) of 6 = −1 -1 -2 1. 2. ∞ 3. f(x) = Σ (−1)″-1. n=1 3. ∞ 4. f(x) = Σ (−1)n-1. n=1 == = 4. = 5. ∞ 1 3 n=1 Σ(-1)-1 22n 2n 1 2n-1 n - 1 Σ (1)n-1. n=1 f(x) = f(x) = Σn=0 f(x) = Σn=0_n! f(x) = Σn=0 (-1)" 2n n! xn+1 2n (-1)" (2n)! (part 3 of 4) Find the Taylor series centered at the origin for the function - 22n-1 (2n-1)! x = x cos(2x). f(x) = En=0 22n f(x) = Σ=0 (2n)! 2n (n − 1)! 1 (2n)! 1 xn (n − 1)! x²n xn xn+1 x²n+1 (-1)" 22n (2n)! x²n+1 x²n 2n x²n xn x²n+1
Transcribed Image Text:(part 1 of 4) Find the coefficient of 6 in the Taylor series expansion centered at the origin for the function f(x) = 6+2 sin(x²). 1. coefficient 2. coefficient ofx6 3. 4. 5. coefficient ofx6 = 2 on (-∞, ∞). = 1 coefficient ofx6 = 3 coefficient ofx6 (part 2 of 4) Find a power series representation for the function f(x) = x sin(2x) 1. f(x) = Σ (−1)n-1. n=1 5. f(x) ∞ 2. f(x) = Σ (-1)″-1. n=1 6. f(x) of 6 = −1 -1 -2 1. 2. ∞ 3. f(x) = Σ (−1)″-1. n=1 3. ∞ 4. f(x) = Σ (−1)n-1. n=1 == = 4. = 5. ∞ 1 3 n=1 Σ(-1)-1 22n 2n 1 2n-1 n - 1 Σ (1)n-1. n=1 f(x) = f(x) = Σn=0 f(x) = Σn=0_n! f(x) = Σn=0 (-1)" 2n n! xn+1 2n (-1)" (2n)! (part 3 of 4) Find the Taylor series centered at the origin for the function - 22n-1 (2n-1)! x = x cos(2x). f(x) = En=0 22n f(x) = Σ=0 (2n)! 2n (n − 1)! 1 (2n)! 1 xn (n − 1)! x²n xn xn+1 x²n+1 (-1)" 22n (2n)! x²n+1 x²n 2n x²n xn x²n+1
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