Use that result to find the power series representation of the integral ſ 1+x¹ dx and determine its radius of convergence. sion to determine its

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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4. The following problem is an example of WHY we want to write functions as power series
1
1+xª
i) The following statement is true: The antiderivative of the function f(x)=
to have to take my word for it, but you can try to find it if you want to)
ii) We will need sometimes to calculate the following integral: ₁ dx
S
1+x4
1
We found in class that
1+x
8
=
-Σ(-1)
n=0
(-1)"x" = 1+x+x² + x³ +....
DOES NOT exist (you are just going
x<1 (converges)
1
Use that result to find the power series representation of the integral
1+x
(So even though we cannot find the antiderivative of the function f(x), we can still write an expression to determine its
integral, and that is pretty awesome!)
dx and determine its radius of convergence.
4
Transcribed Image Text:4. The following problem is an example of WHY we want to write functions as power series 1 1+xª i) The following statement is true: The antiderivative of the function f(x)= to have to take my word for it, but you can try to find it if you want to) ii) We will need sometimes to calculate the following integral: ₁ dx S 1+x4 1 We found in class that 1+x 8 = -Σ(-1) n=0 (-1)"x" = 1+x+x² + x³ +.... DOES NOT exist (you are just going x<1 (converges) 1 Use that result to find the power series representation of the integral 1+x (So even though we cannot find the antiderivative of the function f(x), we can still write an expression to determine its integral, and that is pretty awesome!) dx and determine its radius of convergence. 4
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