Use the Alternating Series Estimation Theorem or Taylor's Formula to estimate the range of values of a for which the given approximation is accurate to within the stated error. Check your answer graphically. (Round your answers to three decimal places.) (error] < 0.001) We know that sin xx I sin x = x -164 120 x³ 6 2²³ + 3! By the Alternating Series Estimation Theorem, the error in the approximation sin x = x= less than Chapter 6 Prot notx 1. x <ょく 1 5! Since we want [error] < 0.00000001, then we mus solve -25 - 25 <0.00012 X Taking the fifth root of a we have that x < 0.065439. When rounded to three decimal places, this gives a range of values for a as 164 X 12 Chapter 6 Prot < 0.00000001, which gives us notx
Use the Alternating Series Estimation Theorem or Taylor's Formula to estimate the range of values of a for which the given approximation is accurate to within the stated error. Check your answer graphically. (Round your answers to three decimal places.) (error] < 0.001) We know that sin xx I sin x = x -164 120 x³ 6 2²³ + 3! By the Alternating Series Estimation Theorem, the error in the approximation sin x = x= less than Chapter 6 Prot notx 1. x <ょく 1 5! Since we want [error] < 0.00000001, then we mus solve -25 - 25 <0.00012 X Taking the fifth root of a we have that x < 0.065439. When rounded to three decimal places, this gives a range of values for a as 164 X 12 Chapter 6 Prot < 0.00000001, which gives us notx
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
Subject: calculus
![Use the Alternating Series Estimation Theorem or Taylor's Formula to estimate the range of values
of a for which the given approximation is accurate to within the stated error. Check your answer
graphically. (Round your answers to three decimal places.)
(error] < 0.001)
We know that
sin xx
1
sin x = x-
-.164
25
120
1
3!
By the Alternating Series Estimation Theorem, the error in the approximation sin x = x-
less than
2³ +
x <<
Chanter & Drnt. nntv
1.
Since we want [error] < 0.00000001, then we mus solve
1
5!
-
25 <0.00012 X
Taking the fifth root of a we have that x < 0.065439. When rounded to three decimal places,
this gives a range of values for a as
.164
12 Chanter 6. Drot nntv
1
A
< 0.00000001, which gives us](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5a8374e2-0c11-468f-938f-bf163a68d0f0%2F18457886-8b05-4c95-92fd-23b0d96b1ca7%2Fc2rk6w_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Use the Alternating Series Estimation Theorem or Taylor's Formula to estimate the range of values
of a for which the given approximation is accurate to within the stated error. Check your answer
graphically. (Round your answers to three decimal places.)
(error] < 0.001)
We know that
sin xx
1
sin x = x-
-.164
25
120
1
3!
By the Alternating Series Estimation Theorem, the error in the approximation sin x = x-
less than
2³ +
x <<
Chanter & Drnt. nntv
1.
Since we want [error] < 0.00000001, then we mus solve
1
5!
-
25 <0.00012 X
Taking the fifth root of a we have that x < 0.065439. When rounded to three decimal places,
this gives a range of values for a as
.164
12 Chanter 6. Drot nntv
1
A
< 0.00000001, which gives us
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