In this problem, you will compute an approximation to 1004 using the degree 2 Taylor polynomial. (a) What function will you use for your approximation, and where will your center be for your approximation? (b) Find the degree 2 Taylor polynomial approximation of your function at the center you chose. You do not need to simplify it, but you must clearly write out each term. (c) Finally, use the degree 2 Taylor polynomial approximation you found in (b) to approximate 1004. You may leave your answer as a sum of numbers. You do no need to simplify it, but you must clearly write out each term.
In this problem, you will compute an approximation to 1004 using the degree 2 Taylor polynomial. (a) What function will you use for your approximation, and where will your center be for your approximation? (b) Find the degree 2 Taylor polynomial approximation of your function at the center you chose. You do not need to simplify it, but you must clearly write out each term. (c) Finally, use the degree 2 Taylor polynomial approximation you found in (b) to approximate 1004. You may leave your answer as a sum of numbers. You do no need to simplify it, but you must clearly write out each term.
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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![In this problem, you will compute an approximation to \( \sqrt[3]{1004} \) using the degree 2 Taylor polynomial.
(a) What function will you use for your approximation, and where will your center be for your approximation?
(b) Find the degree 2 Taylor polynomial approximation of your function at the center you chose. You do not need to simplify it, but you must clearly write out each term.
(c) Finally, use the degree 2 Taylor polynomial approximation you found in (b) to approximate \( \sqrt[3]{1004} \). You may leave your answer as a sum of numbers. You do not need to simplify it, but you must clearly write out each term.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3b47e7c-f6ee-4dde-9ef1-0f8b8a2d2829%2F91636d49-8478-4b0f-8c9c-9ddb57ae62dd%2F2asm13j_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In this problem, you will compute an approximation to \( \sqrt[3]{1004} \) using the degree 2 Taylor polynomial.
(a) What function will you use for your approximation, and where will your center be for your approximation?
(b) Find the degree 2 Taylor polynomial approximation of your function at the center you chose. You do not need to simplify it, but you must clearly write out each term.
(c) Finally, use the degree 2 Taylor polynomial approximation you found in (b) to approximate \( \sqrt[3]{1004} \). You may leave your answer as a sum of numbers. You do not need to simplify it, but you must clearly write out each term.
Expert Solution
Step 1
Given find using the degree 2 Taylor polynomial.
(a) we will use Taylor polynomial of degree 2 and centered at x=a.
f(x)=f(a) +(x-a)+(x-a)2
(b) let f(x)=x 1/3
let center a=1
f'(x)=x-2/3
f"(x)=()x-2/3-1= x-5/9
now f(1)=1
f'(1)=
f"(1)=
Hence, Taylor polynomial is
f(x)= f(a) +(x-a)+(x-a)2
f(x)= 1+(x-1)+()(x-1)2
f(x)= 1+(x-1)-(x-1)2 ---------(1)
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