1.D using root test 2PRACTICE EXERCISES FOR $11.8, §11.9, AND §11.101. Find the radius of convergence and interval of convergence of the power series.1TD12"an= (x+3)ant) - (x+2) • 4²(n+1) ₂2 (1+1)an (ntl)(a)(b)(c)(d)M8 M8 IM8 IM8 IM1n2n(e) Σn=0n²222-1-1 (0*-n!(x+2)²²a=2lim /01/2+1/1 = 1 im 2(71) √x+2) = 1/-4x+2) =호 금1/2 -1x+²2) = 12x+1²1 1/2 x=2 x=1(3x - 1)"(x-3)"(n+1)"3n12n+1-xn-(x-1) 2n2. Find the Taylor series of the function f(x) at the point a.(a) f(x) = ²x, a=11(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)=2na=3

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Answered: (d) n=0 M8 u(I + u) 3n -X

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(d) n=0 M8 u(I + u) 3n -X

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

1.D using root test

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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