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3- Determine the Lagrange polynomial that interpolates the data in the following table 2 4 y 1 -1 3 4

3- Determine the Lagrange polynomial that interpolates the data in the following table 2 4 y 1 -1 3 4

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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3- Determine the Lagrange polynomial that interpolates the data in the following table 2 4 6. y 1 -1 3 4 4- Let f (x) = 2x² e* +1. Construct a Lagrange polynomial of degree two or less using x, = 0, x, = 0.5 and x, = 1. Approximate f (0.8) 5- Determine the polynomial of degree <5, using Newton's divided- differences, that interpolate the data in the following table 1.0 2.0 3.0 4.0 5.0 6.0 f (x) 14.5 19.5 30.5 53.5 94.5 159.5 Use the resulting polynomial to estimate the value of f (4.5). Compare with the exact value, f (4.5) = 71.375. 6- To investigate the relationship between yield of potatoes, y, and level of fertilizer application, x, an experimenter divided a field into 5 pots of equal size and applied differing amounts of fertilizer to each. The data recorded for each plot are given by the table (in Kgs). X 1.0 2.0 3.0 4.0 5.0 y 22 23 25 30 28 - 1 - a) Find an interpolation polynomial for this table. b) According to the interpolating polynomial, approximately how many Kgs would you expect from a plot to which 2.5 Kgs of fertilizer had been applied?
Transcribed Image Text:3- Determine the Lagrange polynomial that interpolates the data in the following table 2 4 6. y 1 -1 3 4 4- Let f (x) = 2x² e* +1. Construct a Lagrange polynomial of degree two or less using x, = 0, x, = 0.5 and x, = 1. Approximate f (0.8) 5- Determine the polynomial of degree <5, using Newton's divided- differences, that interpolate the data in the following table 1.0 2.0 3.0 4.0 5.0 6.0 f (x) 14.5 19.5 30.5 53.5 94.5 159.5 Use the resulting polynomial to estimate the value of f (4.5). Compare with the exact value, f (4.5) = 71.375. 6- To investigate the relationship between yield of potatoes, y, and level of fertilizer application, x, an experimenter divided a field into 5 pots of equal size and applied differing amounts of fertilizer to each. The data recorded for each plot are given by the table (in Kgs). X 1.0 2.0 3.0 4.0 5.0 y 22 23 25 30 28 - 1 - a) Find an interpolation polynomial for this table. b) According to the interpolating polynomial, approximately how many Kgs would you expect from a plot to which 2.5 Kgs of fertilizer had been applied?
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