A scientist has executed one experiment to identify the values of an unknown function f(x). The result of the experiment is tabulated in Table 1: Table 1. Experiment result of unknown function 0.1761 1.5000 0.4772 3.0000 0.0000 0.3010 0.5441 3.5000 f(x) 1.0000 2.0000 a) Based on Table 1, write the Newton's Interpolating Polynomial formula of degree four. b) Identify the coefficient of bo, bị and b; for the Newton's Interpolating Polynomials of degree four by showing the formula and the workflow.
A scientist has executed one experiment to identify the values of an unknown function f(x). The result of the experiment is tabulated in Table 1: Table 1. Experiment result of unknown function 0.1761 1.5000 0.4772 3.0000 0.0000 0.3010 0.5441 3.5000 f(x) 1.0000 2.0000 a) Based on Table 1, write the Newton's Interpolating Polynomial formula of degree four. b) Identify the coefficient of bo, bị and b; for the Newton's Interpolating Polynomials of degree four by showing the formula and the workflow.
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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Transcribed Image Text:QUESTION 1
A scientist has executed one experiment to identify the values of an unknown function f(x). The
result of the experiment is tabulated in Table 1:
Table 1. Experiment result of unknown function
0.0000
1.0000
f(x)
0.1761
0.3010
0.4772
0.5441
1.5000
2.0000
3.0000
3.5000
а)
Based on Table 1, write the Newton's Interpolating Polynomial formula of degree four.
b)
Identify the coefficient of bo, bi and b2 for the Newton's Interpolating Polynomials of
degree four by showing the formula and the workflow.
Identify the coefficient of b; and b4 for the Newton's Interpolating Polynomials of degree
four by showing the formula and the workflow.
c)
d)
Substitute all the coefficients in the equation that you have written in part (a).
Estimate the unknown function with the value of x = 2.5 by using the Newton's
Interpolating Polynomials of degree four.
e)
f)
Find the absolute error of the estimation if log10 x have been identified as the actual value
of the unknown function.
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