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

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter4: Polynomial And Rational Functions
Section4.6: Variation
Problem 16E
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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
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.
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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