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Time (x₁) 0 Value 500 000 (y-f(x)) 1 2 3 375 000 281 250 210 938 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. 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 xo = 0 as the starting node of the polynomial.

Time (x₁) 0 Value 500 000 (y-f(x)) 1 2 3 375 000 281 250 210 938 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. 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 xo = 0 as the starting node of the polynomial.

Advanced Engineering Mathematics
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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Apply 2 decimal places rounding where applicable 

Time (x₁) Value (y₁ = f(xi)) 0 500 000 1 2 281 250 375 000 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. 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 xo = 0 as the starting node of the polynomial. c) Estimate the error in the approximation in Part b). ENG
Transcribed Image Text:Time (x₁) Value (y₁ = f(xi)) 0 500 000 1 2 281 250 375 000 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. 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 xo = 0 as the starting node of the polynomial. c) Estimate the error in the approximation in Part b). ENG
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Since there are multipart, therefore here solutions of part (a) and (b).

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