Given the table of xi and f(xi):0.20.40.60.81.01.2f(x)0.2030.4230.6841.031.5572.572Compute the forward differences to order four and find f(0.73) from a cubic interpolating polynomial.0.1210.8950.5450.232

The forward difference is nothing but the difference of consecutive terms. The forward difference is…

Answered: Given the table of xi and f(xi): 0.2…

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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From the table below find the pressure of the steam at 152 derees C, using newton divided difference polynomial Temp °C (x) Pressure in kgf | cm² (f(x)) 140 150 160 170 3.685 4.854 6.302 8.076
97
Q1/ From the following set of data: A) Calculate f(0.25), using Newton's divided difference formula B) Calculate f (0.25), using Newton-Gauss interpolation method C) Calculate the slope of the polynomial equation at f (0.25) X 0.20 0.22 0.24 0.26 0.28 0.30 0.32 f x) 1.6596 1.6698 1.6804 1.6941 1.7028 1.7146 1.7268
Consider the given graph of the function f(x) over the interval [1,9]. Which one of the following best describes the approximate area between the graph of f(x) and the x-axis over the interval using the sum of 4 even width rectangles, if the height of each rectangle was calculated using the right endpoint of each sub-interval?
Use the Newton forward difference formula to construct interpolating polynomials of degree three for the following data. Approximate f(-0.3) f(-0.75) = -0.0718, f(-0.5) = -0.0247, f(-0.25) = 0.3349, f(0) = 1.1010
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. Use Neville’s method to obtain the approximations for Lagrange interpolating polynomials of degreesone, two, and three to approximate each of the following:a. f (8.4) if f (8.1) = 16.94410, f (8.3) = 17.56492, f (8.6) = 18.50515, f (8.7) = 18.82091b. f −13if f (−0.75) = −0.07181250, f (−0.5) = −0.02475000, f (−0.25) = 0.33493750,f (0) = 1.10100000c. f (0.25) if f (0.1) = 0.62049958, f (0.2) = −0.28398668, f (0.3) = 0.00660095, f (0.4) =0.24842440d. f (0.9) if f (0.6) = −0.17694460, f (0.7) = 0.01375227, f (0.8) = 0.22363362, f (1.0) =0.65809197
6. Consider the function f (x) 1 , x > 0. %3D x + 2 (a) Find the interpolating polynomial P2(x) that agrees with f at the points X1 = 0, x2 = 1, x3 = 2. (You may use Lagrange's interpolation formula or Newton's divided differences formula). (b) Use the above polynomial P2(x) to approximate f(1.5). (c) Find an upper bound for the error |f(1.5) – P2(1.5)| using the appropriate error formula and compare your result with the actual error.
Use appropriate Lagrange interpolating polynomial to approximate f(8.2), if f(8.1) = 16.94, f(8.3) = 17.56, f(8.6) = 18.51, f(8.7) = 18.82
Q1. Given the data in the table below + 1.6 2.5 3.2 4 4.5 f(x) 2 14 15 8 Calculate f(2.8) using Lagrange interpolating polynomials of order 2 and 3. 2. 2/8
Calculate the Laplace transform. Indicate the domain

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Given the table of xi and f(xi): 0.2 0.4 0.6 0.8 1.0 1.2 f(x) 0.203 0.423 0.684 1.03 1.557 2.572 Compute the forward differences to order four and find f(0.73) from a cubic interpolating polynomial. 0.121 0.895 0.545 0.232