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4. Using the definition of a Taylor series, find the Taylor series generated by f(x) centred at x = 5. <-x

4. Using the definition of a Taylor series, find the Taylor series generated by f(x) centred at x = 5. <-x

Advanced Engineering Mathematics
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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4. Using the definition of a Taylor series, find the Taylor series generated by f(x) centred at x = 5. 5. By replacing a with 2r in the Maclaurin series for sinx, we can see that (-1) 22n+12+1 (2n + 1)! sin (2x) = (a) Use the fact that sin²x = that cos r (-1)"2 (2n)! 71=0 (b) Use the fact that sin(2x). 71=0 In this question, you will find another path towards determining the Maclaurin series for sin (2x). = 1-cos(2) 2 <-x to obtain the Maclaurin series for sin² x. Note d sin²x = 2 sin x cos x = sin(2x) to obtain the Maclaurin series for dx
Transcribed Image Text:4. Using the definition of a Taylor series, find the Taylor series generated by f(x) centred at x = 5. 5. By replacing a with 2r in the Maclaurin series for sinx, we can see that (-1) 22n+12+1 (2n + 1)! sin (2x) = (a) Use the fact that sin²x = that cos r (-1)"2 (2n)! 71=0 (b) Use the fact that sin(2x). 71=0 In this question, you will find another path towards determining the Maclaurin series for sin (2x). = 1-cos(2) 2 <-x to obtain the Maclaurin series for sin² x. Note d sin²x = 2 sin x cos x = sin(2x) to obtain the Maclaurin series for dx
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