a) Construct a divided difference table for the ab data. b) Use the table presented in Part a), along with Newton's divided difference formula, to approximate f(2.57 with a polynomial of degree 3, P3(x). Use_x₁ = 0 as the starting node of the polynomial. c) Estimate the error in the approximation in Part
a) Construct a divided difference table for the ab data. b) Use the table presented in Part a), along with Newton's divided difference formula, to approximate f(2.57 with a polynomial of degree 3, P3(x). Use_x₁ = 0 as the starting node of the polynomial. c) Estimate the error in the approximation in Part
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
![a) Construct a divided difference table for the above
data.
b) Use the table presented in Part a), along with
Newton's divided difference formula, to approximate f(2.5)
with a polynomial of degree 3, P3(x). Use x₁ = 0 as the
starting node of the polynomial.
c) Estimate the error in the approximation in Part](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff718c5c4-bf6b-4fda-8e15-e0bd9089f6d3%2Ff67bd9e7-1a7e-4a26-bc95-dc4946d21fb0%2Fvbfxtt5_processed.jpeg&w=3840&q=75)
Transcribed Image Text:a) Construct a divided difference table for the above
data.
b) Use the table presented in Part a), along with
Newton's divided difference formula, to approximate f(2.5)
with a polynomial of degree 3, P3(x). Use x₁ = 0 as the
starting node of the polynomial.
c) Estimate the error in the approximation in Part
![Time
(x₂)
Value
(yi = f(xi))
0
1
2
500 000 375 000 281 250
3
210 938
4
158 203
depicts the value (in Rands) of an automobile at
intervals of 1 year over a period of 4 years. Here
i = 0,1,2,...,4 while the quantities xo = 0 and yo = 500 000,
respectively, represent the time of purchase and
purchase price of the automobile.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff718c5c4-bf6b-4fda-8e15-e0bd9089f6d3%2Ff67bd9e7-1a7e-4a26-bc95-dc4946d21fb0%2F4akywpp_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Time
(x₂)
Value
(yi = f(xi))
0
1
2
500 000 375 000 281 250
3
210 938
4
158 203
depicts the value (in Rands) of an automobile at
intervals of 1 year over a period of 4 years. Here
i = 0,1,2,...,4 while the quantities xo = 0 and yo = 500 000,
respectively, represent the time of purchase and
purchase price of the automobile.
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