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5. Use appropriate Lagrange interpolating polynomials of degrees one, two, and three to approximate each of the following: f (8.4) if f(8.1) = 16.94410, f(8.3) = 17.56492, f (8.6) = 18.50515, f(8.7) = 18.82091 a.

5. Use appropriate Lagrange interpolating polynomials of degrees one, two, and three to approximate each of the following: f (8.4) if f(8.1) = 16.94410, f(8.3) = 17.56492, f (8.6) = 18.50515, f(8.7) = 18.82091 a.

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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5. Use appropriate Lagrange interpolating polynomials of degrees one, two, and three to approximate each of the following: f (8.4) if f(8.1) = 16.94410, f(8.3) = 17.56492, f (8.6) = 18.50515, f (8.7) = 18.82091 b. f (-) if f(-0.75) = -0.07181250, f(-0.5) = -0.02475000, f(-0.25) = 0.33493750, f (0) = 1.10100000 f (0.25) if f(0.1) а. = 0.62049958, f(0.2) = -0.28398668, f(0.3) = 0.00660095, f(0.4) = с. 0.24842440 d. f (0.9) if f(0.6) = -0.17694460, f(0.7) = 0.01375227, f(0.8) = 0.22363362, f(1.0) = 0.65809197 7. The data for Exercise 5 were generated using the following functions. Use the error formula to find a bound for the error, and compare the bound to the actual error for the cases n = 1 and n 2. f(x) = x In x f (x) = x + 4.001lx? + 4.002r + 1.101 f(x) = x cos x - 2r2 +3x - 1 а. b. с. d. f(x) = sin(e - 2)
Transcribed Image Text:5. Use appropriate Lagrange interpolating polynomials of degrees one, two, and three to approximate each of the following: f (8.4) if f(8.1) = 16.94410, f(8.3) = 17.56492, f (8.6) = 18.50515, f (8.7) = 18.82091 b. f (-) if f(-0.75) = -0.07181250, f(-0.5) = -0.02475000, f(-0.25) = 0.33493750, f (0) = 1.10100000 f (0.25) if f(0.1) а. = 0.62049958, f(0.2) = -0.28398668, f(0.3) = 0.00660095, f(0.4) = с. 0.24842440 d. f (0.9) if f(0.6) = -0.17694460, f(0.7) = 0.01375227, f(0.8) = 0.22363362, f(1.0) = 0.65809197 7. The data for Exercise 5 were generated using the following functions. Use the error formula to find a bound for the error, and compare the bound to the actual error for the cases n = 1 and n 2. f(x) = x In x f (x) = x + 4.001lx? + 4.002r + 1.101 f(x) = x cos x - 2r2 +3x - 1 а. b. с. d. f(x) = sin(e - 2)
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