1. Find the radius of converg Σ (x+2)" a=2 n=1 lim lantis-pie (a) 1 n2n
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.3: Geometric Sequences
Problem 81E
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Question
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PRACTICE EXERCISES FOR $11.8, §11.9, AND §11.10
1. Find the radius of convergence and interval of convergence of the power series.
1
TD
12"
an= (x+3)
ant) - (x+2) • 4²
(n+1) ₂2 (1+1)
an (ntl)
(a)
(b)
(c)
(d)
M8 M8 IM8 IM8 IM
1
n2n
(e) Σ
n=0
n²2
22-1-1 (0*-
n!
(x+2)²²a=2
lim /01/2+1/1 = 1 im 2(71) √x+2) = 1/-4x+2) =
호 금
1/2 -1x+²2) = 12x+1²1 1/2 x=2 x=1
(3x - 1)"
(x-3)"
(n+1)"
3n
1
2n+1
-xn
-(x-1) 2n
2. Find the Taylor series of the function f(x) at the point a.
(a) f(x) = ²x, a=1
1
(b) f(x) =
1-x
(c) f(x) = lnx,
3. Find the Maclaurin series of the function f(x).
a=2
(x+2) ++^)
(x+2ja (^+1)=2
n
a=3](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F7534f13a-064e-4169-8c87-38e5472c444f%2F76f59f8d-caac-4945-b21b-5c537dffdd18%2F5vjbu6w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:2
PRACTICE EXERCISES FOR $11.8, §11.9, AND §11.10
1. Find the radius of convergence and interval of convergence of the power series.
1
TD
12"
an= (x+3)
ant) - (x+2) • 4²
(n+1) ₂2 (1+1)
an (ntl)
(a)
(b)
(c)
(d)
M8 M8 IM8 IM8 IM
1
n2n
(e) Σ
n=0
n²2
22-1-1 (0*-
n!
(x+2)²²a=2
lim /01/2+1/1 = 1 im 2(71) √x+2) = 1/-4x+2) =
호 금
1/2 -1x+²2) = 12x+1²1 1/2 x=2 x=1
(3x - 1)"
(x-3)"
(n+1)"
3n
1
2n+1
-xn
-(x-1) 2n
2. Find the Taylor series of the function f(x) at the point a.
(a) f(x) = ²x, a=1
1
(b) f(x) =
1-x
(c) f(x) = lnx,
3. Find the Maclaurin series of the function f(x).
a=2
(x+2) ++^)
(x+2ja (^+1)=2
n
a=3
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