(a) Use differentiation to find a power series representation for f(x) = 1 (5+ x)²* 00 (-1)" nx n 1 f(x) = Σ n = 0 5n+1 What is the radius of convergence, R? R = 5 (b) Use part (a) to find a power series for f(x) 00 f(x) = Σ n = 0 = 1 (5+ x)³° (-1)"n(n-1)x-2 5n+1 What is the radius of convergence, R? R = 5 (c) Use part (b) to find a power series for f(x) = f(x) = 00 n = 2 x² (5 + x)3* (−1)"n(n-1)x" 5n+1 What is the radius of convergence, R? R = 5 ) Enhanced Feedback Please try again, keeping in mind that you can differentiate both sides of the power series expansion to obtain power series representation for the derivative of the given function. So, to find the power series representation of a function of the form you may first find the power series representation of the function The resulting power series converges on the same interval. a (b+cx)2' a b+cx A graphing calculator is recommended. Find a power series representation for f. (Give your power series representation centered at x = 0.) f(x)= = x + 1 00 f(x) = (-1)x4 4n+5 Σ n = 0 Graph f and several partial sums s,(x) on the same screen. What happens as n increases? (Enter your answer using interval notation.) As n increases, s,(x) approximates f better on the interval of convergence, which is (-1,1)

(a) Use differentiation to find a power series representation for f(x) = 1 (5+ x)²* 00 (-1)" nx n 1 f(x) = Σ n = 0 5n+1 What is the radius of convergence, R? R = 5 (b) Use part (a) to find a power series for f(x) 00 f(x) = Σ n = 0 = 1 (5+ x)³° (-1)"n(n-1)x-2 5n+1 What is the radius of convergence, R? R = 5 (c) Use part (b) to find a power series for f(x) = f(x) = 00 n = 2 x² (5 + x)3* (−1)"n(n-1)x" 5n+1 What is the radius of convergence, R? R = 5 ) Enhanced Feedback Please try again, keeping in mind that you can differentiate both sides of the power series expansion to obtain power series representation for the derivative of the given function. So, to find the power series representation of a function of the form you may first find the power series representation of the function The resulting power series converges on the same interval. a (b+cx)2' a b+cx A graphing calculator is recommended. Find a power series representation for f. (Give your power series representation centered at x = 0.) f(x)= = x + 1 00 f(x) = (-1)x4 4n+5 Σ n = 0 Graph f and several partial sums s,(x) on the same screen. What happens as n increases? (Enter your answer using interval notation.) As n increases, s,(x) approximates f better on the interval of convergence, which is (-1,1)

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter5: Inverse, Exponential, And Logarithmic Functions

Section: Chapter Questions

Problem 9T

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