3π (a) Write out the degree 2 Taylor polynomial T₂(x) for f(x)=sin (2x) about center a=³ 8 You may find it helpful to be reminded that sin and cos (37)= -√2 3π √2 Зл 4 2 4 (b) Use the polynomial T₂(x) that you found in part (a) to write down a sum of terms that gives an 7₁ 7T sin 16 8 As part of this process, identify the value of x that you are plugging into T₂(x). approximation to the value of f (c) Use Taylor's Inequality to find an upper bound on the error |R, (x)| when T₂(x) is used to 71 8 You do not need to simplify this sum of terms. 7₁ 16 You do not need to simplify the numerical value of this upper bound. approximate f sin Identify the value of "M" that you are using.
3π (a) Write out the degree 2 Taylor polynomial T₂(x) for f(x)=sin (2x) about center a=³ 8 You may find it helpful to be reminded that sin and cos (37)= -√2 3π √2 Зл 4 2 4 (b) Use the polynomial T₂(x) that you found in part (a) to write down a sum of terms that gives an 7₁ 7T sin 16 8 As part of this process, identify the value of x that you are plugging into T₂(x). approximation to the value of f (c) Use Taylor's Inequality to find an upper bound on the error |R, (x)| when T₂(x) is used to 71 8 You do not need to simplify this sum of terms. 7₁ 16 You do not need to simplify the numerical value of this upper bound. approximate f sin Identify the value of "M" that you are using.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:Зл
(a) Write out the degree 2 Taylor polynomial T₂(x) for f(x)=sin (2x) about center a=- 8
31 √√2
You may find it helpful to be reminded that sin
4
(b) Use the polynomial T₂(x) that you found in part (a) to write down a sum of terms that gives an
7π
7π
approximation to the value of f =sin
16
8
As part of this process, identify the value of x that you are plugging into T₂(x).
3л
|--1/24 and cos (37) = -√2
4
2
(c) Use Taylor's Inequality to find an upper bound on the error R, (x) when T₂(x) is used to
7π
8
approximate f
You do not need to simplify this sum of terms.
7₁
16
You do not need to simplify the numerical value of this upper bound.
=sin
Identify the value of "M" that you are using.
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