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Part 1: Partial Fractions Use the partial fractions method to express the function as a power series (centered at x = 0) and give the open interval of convergence. f(x) 17 x² + 1x - 72 f(x) = (-1/8)(x/8)^n+(-1/9)(-1)^nl n=0 The open interval of convergence is: (-8,8) Give your answer in interval notation. Part 2: Completing the Square Now use the method of completing the square to express the function as a power series and give the natural center and open interval of convergence. f(x) = ∞ Σ n=0 The center is: The open interval of convergence is: Give your answer in interval notation. f(x) = 17 x² + 1x - 72

Part 1: Partial Fractions Use the partial fractions method to express the function as a power series (centered at x = 0) and give the open interval of convergence. f(x) 17 x² + 1x - 72 f(x) = (-1/8)(x/8)^n+(-1/9)(-1)^nl n=0 The open interval of convergence is: (-8,8) Give your answer in interval notation. Part 2: Completing the Square Now use the method of completing the square to express the function as a power series and give the natural center and open interval of convergence. f(x) = ∞ Σ n=0 The center is: The open interval of convergence is: Give your answer in interval notation. f(x) = 17 x² + 1x - 72

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.2: Arithmetic Sequences
Problem 67E
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Part 1: Partial Fractions Use the partial fractions method to express the function as a power series (centered at x = 0) and give the open interval of convergence. 17 x² + 1x - 72 f(x) = ∞ Σ (-1/8)(x/8)^n+(-1/9)(-1)^n( n=0 The open interval of convergence is: (-8,8) Give your answer in interval notation. Part 2: Completing the Square Now use the method of completing the square to express the function as a power series and give the natural center and open interval of convergence. ∞ f(x) = Σ n=0 The center is: ƒ(x) = The open interval of convergence is: Give your answer in interval notation. ƒ(x) = x² 17 + 1x - 72
Transcribed Image Text:Part 1: Partial Fractions Use the partial fractions method to express the function as a power series (centered at x = 0) and give the open interval of convergence. 17 x² + 1x - 72 f(x) = ∞ Σ (-1/8)(x/8)^n+(-1/9)(-1)^n( n=0 The open interval of convergence is: (-8,8) Give your answer in interval notation. Part 2: Completing the Square Now use the method of completing the square to express the function as a power series and give the natural center and open interval of convergence. ∞ f(x) = Σ n=0 The center is: ƒ(x) = The open interval of convergence is: Give your answer in interval notation. ƒ(x) = x² 17 + 1x - 72
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