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2. Using the attached table of Power Functions, find the power function for the given functions and integrate the first 3 terms. s(x) = e sinx

2. Using the attached table of Power Functions, find the power function for the given functions and integrate the first 3 terms. s(x) = e sinx

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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 I need help with number 2.

Using the attached table of Power Functions, find the power function for the given functions and integrate the first 3 terms

 s(x) = e^xsinx

n 2 3 4 5 1. Find the nth Taylor polynomial centered at the given c. Use the included table to show work. a. f(x)=e*,n=4,c=0 n! P₁(x) = f(") (x) f(") (c) (x-c)" f(n) (c) (x-c)" n! 2. Using the attached table of Power Functions, find the power function for the given functions and integrate the first 3 terms. s(x)=e* sinx
Transcribed Image Text:n 2 3 4 5 1. Find the nth Taylor polynomial centered at the given c. Use the included table to show work. a. f(x)=e*,n=4,c=0 n! P₁(x) = f(") (x) f(") (c) (x-c)" f(n) (c) (x-c)" n! 2. Using the attached table of Power Functions, find the power function for the given functions and integrate the first 3 terms. s(x)=e* sinx
Power Series for Elementary Functions Function 1 X 1 1 + x = 1 (x - 1) + (x - 1)²(x - 1)³ + (x − 1)4 - = 1 − x + x² − x³ + x4 – x³ + · · · + (−1)″ x" +... In x = (x - 1) et = 1 + x + sin x = x - cos x = 1 1 arctan x =t- arcsin x = x+ 3! x² 2! x3 3 + 記ざ + + (x - 1)² 2 (1 + x)k = 1 + kx + 5! + 5 x4 x6 4! 6! - x3 x4 + x5 3! 4! 5! + + 1 + + 7! 9! 7 + x8 8! +⁹ x3 1. 3x5 + 2.3 2.4.5 + - 3 + 1)³ k(k + (x - 1)4 4 + + X" + + n! (-1)" x2n+1 (2n + 1)! (-1)" x2n (2n)! 1.3.5x7 2.4.6.7 k(k-1)x² 2! *The convergence at x = ±1 depends on the value of k. +... + (-1)" x²n+1 2n + 1 + 1)(k − 2)x³ 3! -··· + (−1)" (x − 1)" + + + +.. + (-1)"-¹(x - 1)" +... n (2n)!x²n+1 (2"n!)²(2n + 1) +. k(k − 1)(k − 2)(k − 3)x4 4! + + Interval of Convergence 0<x<2 -1<x< 1 0 < x≤2 -∞AXAM -8AHA T8AHA -1≤x≤ -1≤x≤ -1<x<
Transcribed Image Text:Power Series for Elementary Functions Function 1 X 1 1 + x = 1 (x - 1) + (x - 1)²(x - 1)³ + (x − 1)4 - = 1 − x + x² − x³ + x4 – x³ + · · · + (−1)″ x" +... In x = (x - 1) et = 1 + x + sin x = x - cos x = 1 1 arctan x =t- arcsin x = x+ 3! x² 2! x3 3 + 記ざ + + (x - 1)² 2 (1 + x)k = 1 + kx + 5! + 5 x4 x6 4! 6! - x3 x4 + x5 3! 4! 5! + + 1 + + 7! 9! 7 + x8 8! +⁹ x3 1. 3x5 + 2.3 2.4.5 + - 3 + 1)³ k(k + (x - 1)4 4 + + X" + + n! (-1)" x2n+1 (2n + 1)! (-1)" x2n (2n)! 1.3.5x7 2.4.6.7 k(k-1)x² 2! *The convergence at x = ±1 depends on the value of k. +... + (-1)" x²n+1 2n + 1 + 1)(k − 2)x³ 3! -··· + (−1)" (x − 1)" + + + +.. + (-1)"-¹(x - 1)" +... n (2n)!x²n+1 (2"n!)²(2n + 1) +. k(k − 1)(k − 2)(k − 3)x4 4! + + Interval of Convergence 0<x<2 -1<x< 1 0 < x≤2 -∞AXAM -8AHA T8AHA -1≤x≤ -1≤x≤ -1<x<
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