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a. Differentiate the Taylor series about 0 for the function f(x) = 2x b. Identify the function represented by the differentiated series. c. Give the interval of convergence of the power series for the derivative. a. Which of the following is the derivative of the Taylor series about x = 0? 00 Ο Α.Σ k=1 (2)kxk-1 (k-1)! 00 xk-1 Ο c. 2 Σ k=0

a. Differentiate the Taylor series about 0 for the function f(x) = 2x b. Identify the function represented by the differentiated series. c. Give the interval of convergence of the power series for the derivative. a. Which of the following is the derivative of the Taylor series about x = 0? 00 Ο Α.Σ k=1 (2)kxk-1 (k-1)! 00 xk-1 Ο c. 2 Σ k=0

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 50E
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a. Differentiate the Taylor series about 0 for the function f(x) = ²x b. Identify the function represented by the differentiated series. c. Give the interval of convergence of the power series for the derivative. a. Which of the following is the derivative of the Taylor series about x = 0? O A. ∞0 k=1 Ο c. 2 Σ #3 (2)kxk-1 (k-1)! 00 xk-1 (k-1)! k=0 b. What is the function represented by the differentiated series? f(x) = 0 c. What is the interval of convergence? C S4 $ 45 % MacBook Pro Search or type URL ^ 6 & 7 ... 00 Ο Β. Σ k=0 ∞ xk OD. 2 Σ (k-1)! k=1 * xk-1 (k-1)! 8 This que 9
Transcribed Image Text:a. Differentiate the Taylor series about 0 for the function f(x) = ²x b. Identify the function represented by the differentiated series. c. Give the interval of convergence of the power series for the derivative. a. Which of the following is the derivative of the Taylor series about x = 0? O A. ∞0 k=1 Ο c. 2 Σ #3 (2)kxk-1 (k-1)! 00 xk-1 (k-1)! k=0 b. What is the function represented by the differentiated series? f(x) = 0 c. What is the interval of convergence? C S4 $ 45 % MacBook Pro Search or type URL ^ 6 & 7 ... 00 Ο Β. Σ k=0 ∞ xk OD. 2 Σ (k-1)! k=1 * xk-1 (k-1)! 8 This que 9
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