Find the remainder in the Taylor series centered at the point a for the following function. Then show that lim R, (x)=0 for all x in the interval of convergence. 7-8 f(x)=sinx, a=0 Find the remainder. Choose the correct answer below. OA. R(x)=- t sin c (n+1)! OB. R(x)=- t sin c (n+1)! OC. R₁(x)=- OD. R(x)=- OB. O C. O. D. - sinc n+1 (n+1)! n+1 *+1 ± cos c (n+1)! or R, (x)= or R₁ (x)= t cos c n+1 (n+1)! cos c (n+1)! Show that lim R₁(x)=0 for all in the interval of convergence. Choose the correct answer below. n-∞ A. lim R₁(x)=0 because Rn(x)| ≤ (n+1)! S n→∞ n+1 n+1 and lim n18 lim R, (x)=0 because |R₂(x)2 (n+1)! and lim |x| n1x n-∞ 1 lim R₁(x)=0 because |R₁(x) 2 (n+1)! n→∞ lim R₁(x) = 0 because |R(x) s and lim |x| (n+1)! n→∞o n10 -=0 for all x. nx n X n! n! = 0 for all x. = 0 for all x. 1 and lim=0 for all x. n CE
Find the remainder in the Taylor series centered at the point a for the following function. Then show that lim R, (x)=0 for all x in the interval of convergence. 7-8 f(x)=sinx, a=0 Find the remainder. Choose the correct answer below. OA. R(x)=- t sin c (n+1)! OB. R(x)=- t sin c (n+1)! OC. R₁(x)=- OD. R(x)=- OB. O C. O. D. - sinc n+1 (n+1)! n+1 *+1 ± cos c (n+1)! or R, (x)= or R₁ (x)= t cos c n+1 (n+1)! cos c (n+1)! Show that lim R₁(x)=0 for all in the interval of convergence. Choose the correct answer below. n-∞ A. lim R₁(x)=0 because Rn(x)| ≤ (n+1)! S n→∞ n+1 n+1 and lim n18 lim R, (x)=0 because |R₂(x)2 (n+1)! and lim |x| n1x n-∞ 1 lim R₁(x)=0 because |R₁(x) 2 (n+1)! n→∞ lim R₁(x) = 0 because |R(x) s and lim |x| (n+1)! n→∞o n10 -=0 for all x. nx n X n! n! = 0 for all x. = 0 for all x. 1 and lim=0 for all x. n CE
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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Question
Transcribed Image Text:Find the remainder in the Taylor series centered at the point a for the following function. Then show that lim R, (x)=0 for all x in the interval of convergence.
П-00
f(x)=sinx, a=0
Find the remainder. Choose the correct answer below.
OA. R₁(x)=
OB. R(x)=
O C. R₁(x) =
OD. R(x)=
OB.
t sin c
(n+1)!
O C.
t sin c
(n+1)!
OD.
n→∞
n+1
**1
- sinc
(n+1)!
or R, (x)=
or R₁ (x) =
± cos c
(n+1)!
Show that R₁(x)=0 for all in the interval of convergence. Choose the correct answer below.
± cos c
(n+1)!
n+1
cos C
(n+1)!
O A. lim R, (x) = 0 because |R₂(x)| ≤ (n+1)!
n-∞
n+1
lim R₁(x) = 0 because R(x) s
n→∞
n+1
n+1
n+1
|x|"
(n+1)!
|x|
xn
lim R, (x) = 0 because R₁(x)| ² (n+1)! and lim = 0 for all x.
n!
n→∞
n→∞
1
(n+1)!
and lim = 0 for all x.
n
n→∞
and lim
n→∞
lim R₁(x)=0 because R₁(x) 2 and
n∞
n
n-∞
n!
= 0 for all x.
1
lim=0 for all x..
n
Time Remaining: C
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