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Use the power series for the function, centered at 0, and deermine the interval of convergence: f(x) = - 1/(x+1)^2  = d/dx[1/(x+1)]

Use the power series for the function, centered at 0, and deermine the interval of convergence: f(x) = - 1/(x+1)^2  = d/dx[1/(x+1)]

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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Use the power series for the function, centered at 0, and deermine the interval of convergence:

f(x) = - 1/(x+1)^2  = d/dx[1/(x+1)]

Using a Power Series In Exercises 19, 20, 21, 22, 23, 24, 25, 26, 27, and 28, use the power series 1 E(-1)"x", |æ| <1 1+x n=0 to find a power series for the function, centered at 0, and determine the interval of convergence.
Transcribed Image Text:Using a Power Series In Exercises 19, 20, 21, 22, 23, 24, 25, 26, 27, and 28, use the power series 1 E(-1)"x", |æ| <1 1+x n=0 to find a power series for the function, centered at 0, and determine the interval of convergence.
d 21. f (2) = - T+ 1 = (x + 1)² dx x + 1 Answer + d? 22. f (x) (x + 1)* dx? | x + 1 1 23. f (x) = ln (x +1) = x + 1 Answer 24. /(2) = la (1 – =") = / - dx 1+ x 1 -dx 1 25. g (x) = x² + 1 Answer 26. f (x) = ln (x² + 1) 1 27. h (x) = 4x2 +1 Answer 28. f (x) = arctan 2x
Transcribed Image Text:d 21. f (2) = - T+ 1 = (x + 1)² dx x + 1 Answer + d? 22. f (x) (x + 1)* dx? | x + 1 1 23. f (x) = ln (x +1) = x + 1 Answer 24. /(2) = la (1 – =") = / - dx 1+ x 1 -dx 1 25. g (x) = x² + 1 Answer 26. f (x) = ln (x² + 1) 1 27. h (x) = 4x2 +1 Answer 28. f (x) = arctan 2x
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