Q4. Use Newton forward-difference formula andconstruct appropriate interpolating polynomial andapproximate f(0.5)Xi -1 0 1 2fi 1-1113

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Answered: Q4. Use Newton forward-difference…

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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2Q. (b) The set of following data points is given x 1 1.5 2 5.2 y 3.8 4.9 Determine the second order polynomial by using Newton divided difference method.
Q2) The following values of the function f(x) = sin x + cos x are given X 10⁰ 20⁰ 30⁰ 1.3660 f(x) 1.1585 1.2817 Construct the Lagrange interpolation polynomial that fits the data and find (), compare with exact values.
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
P=S/(S+F) Express S in terms of F and P
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
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Find Newton’s polynomial that interpolates f(x) = x1 at x = 1, x=2,x=4,andx=5. Usethetableweusedinclasstofindthe coefficients.
Solve clearly, hand written.
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
Find the interpolating polynomial of the following point and function using Newton's interpolation process. y = ln ( x + 2 ) at x = [-1,2]. Find the interpolating polynomial of the following function using Direct Fit Polynomials. y = exp( 2-x ) at x = [-1,2].
a. Find the linear approximating polynomial for the following function centered at the given point a. b. Find the quadratic approximating polynomial for the following function centered at the given point a. c. Use the polynomials obtained in parts a. and b. to approximate the given quantity. 1 f(x) = 1 --, a = 1; approximate 1.08
Is (f og)(0) = (fg)(0)? Justify answer

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Q4. Use Newton forward-difference formula and construct appropriate interpolating polynomial and approximate f(0.5) Xi -1 0 1 2 fi 1 -1 1 13