35-40. Combining power series Use the power series representation f(x) = In (1 – x) = - for -1 sx< 1, to find the power series for the following functions (centered at 0). Give the interval of convergence of the new series. 35. F(3x) — In (1 — 3х) 37. h(x) — х In (1 — х) 39. p(x) — 2х8 In (1 — х) 36. g(x) = x³ In (1 – x) 38. f(r*) = In (1 – x') 40. f(-4x) = In (1 + 4x)
35-40. Combining power series Use the power series representation f(x) = In (1 – x) = - for -1 sx< 1, to find the power series for the following functions (centered at 0). Give the interval of convergence of the new series. 35. F(3x) — In (1 — 3х) 37. h(x) — х In (1 — х) 39. p(x) — 2х8 In (1 — х) 36. g(x) = x³ In (1 – x) 38. f(r*) = In (1 – x') 40. f(-4x) = In (1 + 4x)
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 44E
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Transcribed Image Text:35-40. Combining power series Use the power series representation
f(x) = In (1 – x) = -
for -1 sx< 1,
to find the power series for the following functions (centered at 0).
Give the interval of convergence of the new series.
35. F(3x) — In (1 — 3х)
37. h(x) — х In (1 — х)
39. p(x) — 2х8 In (1 — х)
36. g(x) = x³ In (1 – x)
38. f(r*) = In (1 – x')
40. f(-4x) = In (1 + 4x)
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