In problems 3-5, use the building block n=0 Σ", <1, together with the result differentiating and integrating power series to find a power series representation for the given function and determine the interval of convergence. 3. f(x) = 1 (1-x)² 4. g(x) = ln (1-x) 5. h(x) = tan-¹ I 6. Integrate dr as a power series. Determine the radius of convergence.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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In problems 3 - 5, use the building block
x", r1, together with the result
I
n=0
differentiating and integrating power series to find a power series representation for the given
function and determine the interval of convergence.
3. f(x) =
4. g(x) = ln(1 x)
5. h(x) = tan-¹
1
(1-x)²
6. Integrate /₁
I
da as a power series. Determine the radius of convergence.
x8
Transcribed Image Text:In problems 3 - 5, use the building block x", r1, together with the result I n=0 differentiating and integrating power series to find a power series representation for the given function and determine the interval of convergence. 3. f(x) = 4. g(x) = ln(1 x) 5. h(x) = tan-¹ 1 (1-x)² 6. Integrate /₁ I da as a power series. Determine the radius of convergence. x8
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