5. If we know that F(x) = Lan(x – c)" for all |r – e| < R for R> 0, then we can use differentiation, integration and substitution to find new power series representations for F'(x), | F(x) dr and F(9(x)). (a) Use the Geometric Series Test to find a power series representation centered at e = 0 for f(x) = 1 1+z²* (b) Use term-by-term differentiation to find a power series representation centered at c = 0 of f'(1). Determine the radius of convergence and the interval of convergence. Determine the radius of convergence and the interval of convergence. 1 (c) Use part (b) to find a power series representation centered at e = 0 for What is the (1+x²)2 ° radius of convergence and the interval of convergence for the power series?

5. If we know that F(x) = Lan(x – c)" for all |r – e| < R for R> 0, then we can use differentiation, integration and substitution to find new power series representations for F'(x), | F(x) dr and F(9(x)). (a) Use the Geometric Series Test to find a power series representation centered at e = 0 for f(x) = 1 1+z²* (b) Use term-by-term differentiation to find a power series representation centered at c = 0 of f'(1). Determine the radius of convergence and the interval of convergence. Determine the radius of convergence and the interval of convergence. 1 (c) Use part (b) to find a power series representation centered at e = 0 for What is the (1+x²)2 ° radius of convergence and the interval of convergence for the power series?

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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