e differentiation to find a power series re f(x) = Σ( n = 0 1 (4 + x)² s the radius of convergence, R? f(x) (-1)" (n+1)x" 42+2 = e part (a) to find a power series for 1 (4 + x)³ V
e differentiation to find a power series re f(x) = Σ( n = 0 1 (4 + x)² s the radius of convergence, R? f(x) (-1)" (n+1)x" 42+2 = e part (a) to find a power series for 1 (4 + x)³ V
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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![(a) Use differentiation to find a power series representation for
f(x) =
f(x)= =
8
f(x):
Σ(
=
n = 0
What is the radius of convergence, R?
R = 4
(b) Use part (a) to find a power series for
1
f(x)
(4 + x) ³
00
Σ(
n = 0
1
(4 + x)²
(-1)" (n+1)x"
42+2
f(x) =
What is the radius of convergence, R?
R = 4
8
(c) Use part (b) to find a power series for
x²
(4 + x)³
f(x) = Σ (
n = 2
(-1)" (n+1)(n+2)x"
2 x 4+3
(-1)" n(n-1)x"
2x 4"+1
What is the radius of convergence, R?
R=
4
X](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb0f3a834-d342-4869-9dbf-9d566abb1119%2F7152cea3-8410-443b-a534-be2067749538%2F6qyvvl9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) Use differentiation to find a power series representation for
f(x) =
f(x)= =
8
f(x):
Σ(
=
n = 0
What is the radius of convergence, R?
R = 4
(b) Use part (a) to find a power series for
1
f(x)
(4 + x) ³
00
Σ(
n = 0
1
(4 + x)²
(-1)" (n+1)x"
42+2
f(x) =
What is the radius of convergence, R?
R = 4
8
(c) Use part (b) to find a power series for
x²
(4 + x)³
f(x) = Σ (
n = 2
(-1)" (n+1)(n+2)x"
2 x 4+3
(-1)" n(n-1)x"
2x 4"+1
What is the radius of convergence, R?
R=
4
X
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