Using the table of Taylor series, derive a power series for f(x) = cos( sqrt |x|). a. Give the first 3 non-zero terms and its general terms. b. Give the radius of convergence without using a ratio test calculation. C. Using the above calculate a power series for g(x) = integral cos( sqrt |x|). No expression here in terms of elementary functions. D. Give the radius of convergence of the new series without using a ratio test calculation. E. Give an intuitive argument predicting the radius of convergence by looking at the general terms. F. Use the series for g (x) to approximate integral of 0 to 1 of cos( sqrt |x|) dx by getting a series for it and evaluating the third partial sum.
Using the table of Taylor series, derive a power series for f(x) = cos( sqrt |x|). a. Give the first 3 non-zero terms and its general terms. b. Give the radius of convergence without using a ratio test calculation. C. Using the above calculate a power series for g(x) = integral cos( sqrt |x|). No expression here in terms of elementary functions. D. Give the radius of convergence of the new series without using a ratio test calculation. E. Give an intuitive argument predicting the radius of convergence by looking at the general terms. F. Use the series for g (x) to approximate integral of 0 to 1 of cos( sqrt |x|) dx by getting a series for it and evaluating the third partial sum.
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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Using the table of Taylor series, derive a power series for f(x) = cos( sqrt |x|). a. Give the first 3 non-zero terms and its general terms. b. Give the radius of convergence without using a ratio test calculation. C. Using the above calculate a power series for g(x) = integral cos( sqrt |x|). No expression here in terms of elementary functions. D. Give the radius of convergence of the new series without using a ratio test calculation. E. Give an intuitive argument predicting the radius of convergence by looking at the general terms. F. Use the series for g (x) to approximate integral of 0 to 1 of cos( sqrt |x|) dx by getting a series for it and evaluating the third partial sum.
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