Use the following information to complete parts a. and b. below. f(x) = 11 Inx, a = 5 a. Find the first four nonzero terms of the Taylor series for the given function centered at a. A. The first four nonzero terms are B. The first four nonzero terms are ∞ Ο A. 11 In 5+ Σ (-1)* . k=0 8 OB. 11 In 5+ (−1)k+1. k=1 11 5*(x-5)k 8 Ο c. 11In 5+ Σ k=1 11 5 D. The first four nonzero terms are 11 In 5- 11 5 11 OC. The first four nonzero terms are 11 In 5+ 5 11 k.5k + 11(-1)+1(x-5)k 5k + -(x - 5)k 11 b. Write the power series using summation notation. 50 11 50 -(x - 5) - (x-5)- 11 5 22 125 -(x-5)- 11 375 11 (x - 5)² + (x - 5)² + -(x − 5)² + 50 33 125 11 2500 11 375 (x - 5)³. 125 (x - 5)³. -(x - 5)³. (x - 5)-(x - 5)²-(x - 5)³.
Use the following information to complete parts a. and b. below. f(x) = 11 Inx, a = 5 a. Find the first four nonzero terms of the Taylor series for the given function centered at a. A. The first four nonzero terms are B. The first four nonzero terms are ∞ Ο A. 11 In 5+ Σ (-1)* . k=0 8 OB. 11 In 5+ (−1)k+1. k=1 11 5*(x-5)k 8 Ο c. 11In 5+ Σ k=1 11 5 D. The first four nonzero terms are 11 In 5- 11 5 11 OC. The first four nonzero terms are 11 In 5+ 5 11 k.5k + 11(-1)+1(x-5)k 5k + -(x - 5)k 11 b. Write the power series using summation notation. 50 11 50 -(x - 5) - (x-5)- 11 5 22 125 -(x-5)- 11 375 11 (x - 5)² + (x - 5)² + -(x − 5)² + 50 33 125 11 2500 11 375 (x - 5)³. 125 (x - 5)³. -(x - 5)³. (x - 5)-(x - 5)²-(x - 5)³.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:Use the following information to complete parts a. and b. below.
f(x) = 11 Inx, a = 5
a. Find the first four nonzero terms of the Taylor series for the given function centered at a.
OA. The first four nonzero terms are
B. The first four nonzero terms are
∞
Ο A. 11 In 5+ Σ (-1)* -
k=0
8
11
OC. The first four nonzero terms are 11 In 5+
5
D. The first four nonzero terms are 11 In 5-
OB. 11 In 5+ (−1)k+1.
k=1
11
5*(x-5)k
8
Ο c. 11In 5+ Σ
k=1
11
5
11
11
5
b. Write the power series using summation notation.
k.5k
+
-(x - 5)k
11(-1)+1(x-5)k
5k
11
50
(x-5)-
11
+ (x-5)-
50
11
5
22
125
-(x-5)-
11
375
11
(x - 5)² +
50
(x - 5)² +
¯(x − 5)² +
33
125
11
2500
11
375
(x - 5)³.
125
¯(x – 5)³.
-(x - 5)³.
(x - 5)-(x - 5)²-(x - 5)³.
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