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Given the Maclaurin series for cos x : (-1)" -2²n COs x = (2n)! n=0 (i) Find the Maclaurin series for :f(x) = (1+x²) cos æ. (ii) Write down the interval of convergence of the Maclaurin series for f(x)? (iii) Using the nth coefficient of the Maclaurin series for f(x) in part (i), determine f(2n) (0) and f(2n+1) (0), in terms of n. (iv) Using results in part (iii), Find f(12) (0) and f(1201) (0). Give all necessary steps

Given the Maclaurin series for cos x : (-1)" -2²n COs x = (2n)! n=0 (i) Find the Maclaurin series for :f(x) = (1+x²) cos æ. (ii) Write down the interval of convergence of the Maclaurin series for f(x)? (iii) Using the nth coefficient of the Maclaurin series for f(x) in part (i), determine f(2n) (0) and f(2n+1) (0), in terms of n. (iv) Using results in part (iii), Find f(12) (0) and f(1201) (0). Give all necessary steps

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 49E
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Given the Maclaurin series for cos : Š (-1)" 00 2n COs x = ·x² (2n)! (i) Find the Maclaurin series for : f(x) = (1+x²) cos x. (ii) Write down the interval of convergence of the Maclaurin series for f(x)? (iii) Using the nth coefficient of the Maclaurin series for f(x) in part (i), determine f(2n) (0) and f(2n+1) (0), in terms of n. (iv) Using results in part (ii) Find f(12)(0) and f(1201) (0). Give all necessary steps
Transcribed Image Text:Given the Maclaurin series for cos : Š (-1)" 00 2n COs x = ·x² (2n)! (i) Find the Maclaurin series for : f(x) = (1+x²) cos x. (ii) Write down the interval of convergence of the Maclaurin series for f(x)? (iii) Using the nth coefficient of the Maclaurin series for f(x) in part (i), determine f(2n) (0) and f(2n+1) (0), in terms of n. (iv) Using results in part (ii) Find f(12)(0) and f(1201) (0). Give all necessary steps
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