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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
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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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
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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