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Given the data x 1.6 2 2.2 4 4.5 f(x) 2 8 14 15 8 2 Calculate f(2.8) using Newton's interpolating polynomials of order 1 through 3.

Given the data
x
1.6 2 2.5 3.2 4 4.5
f(x) 2 8 14 15 8 2

Calculate f(2.8) using Newton’s interpolating polynomials of order 1
through 3. Choose the sequence of the points for your estimates to attain
the best possible accuracy.

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