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 series1E(-1)"x", |æ| <11+xn=0to find a power series for the function, centered at 0, and determine the interval of convergence. d21. f (2) = - T+ 1 =(x + 1)²dx x + 1Answer +d?22. f (x)(x + 1)*dx? | x + 1123. f (x) = ln (x +1) =x + 1Answer24. /(2) = la (1 – =") = / -dx1+ x1-dx125. g (x) =x² + 1Answer26. f (x) = ln (x² + 1)127. h (x) =4x2 +1Answer28. f (x) = arctan 2x

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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)]

College Algebra

10th Edition

ISBN:9781337282291

Author:Ron Larson

Publisher:Ron Larson

Chapter8: Sequences, Series,and Probability

Section: Chapter Questions

Problem 18RE: Finding the Sum of an Infinite Series In Exercises 17 and 18, find the sum of the infinite series....

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Question

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.

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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