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need help with number 1. The table to use is attached.

need help with number 1. The table to use is attached.

Algebra for College Students
Algebra for College Students
10th Edition
ISBN:9781285195780
Author:Jerome E. Kaufmann, Karen L. Schwitters
Publisher:Jerome E. Kaufmann, Karen L. Schwitters
Chapter9: Polynomial And Rational Functions
Section9.2: Remainder And Factor Theorems
Problem 53PS
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I need help with number 1. The table to use is attached. 

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<
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
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