Obtain the Lagrange interpolating polynomial using all the data points below: Obtain the Lagrange interpolating polynomial using all the data points below:0.51.01.52.02.5f(x)0.84150.90930.1411-0.7568-0.9589

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Answered: Obtain the Lagrange interpolating…

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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An open-top box is to be constructed from a sheet of tin that measures 18 inches by 10 inches by cutting out squares from each corner as shown and then folding up the sides. Let V(x) denote the volume of the resulting box. w = 10 inches | = 18 inches Step 1 of 2: Write V(x) as a product of linear factors.
Using the data in the table, with the help of Lagrange Interpolation Polynomials, 3.Obtain a polynomial of degrees P (0.75) =? , P (1.25) =? , P (1.5) =? valuesFind.
Q1-Using the nodes (x=2, x=2.5 and x; =4), to find the second interpolation polynomial for f(x) =- O O D
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The following data gives the melting points of an alloy of lead and zinc. Find the melting point of the alloy containing 54% of lead by Newton’s forward interpolating polynomial.
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Suppose experimental data are represented by a set of points in the plane. An interpolating polynomial for the data is a polynomial whose graph passes through every point. In scientific work, such a polynomial can be used, for example, to estimate values between the known data points. Another use is to create curves for graphical images on a computer screen. One method for finding an interpolating polynomial is to solve a system of linear equations. Find the interpolating polynomial of (SEE PICTURE)
Q2. (a) Compare and contrast the following four interpolated polynomials. Lagrange Polynomial. (i) (ii) Newton Divided-Difference Polynomial. (iii) Hermite Polynomial. (iv) Cubic Spline Polynomial.
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Use Algorithm 3.2 (Divided Difference) to construct the interpolating polynomial of degree three for the following data: f(1) = 1.2,f(2)= 1.6,f(4)=2, and f(5)=2.6 , then f(2.6)
use excel and submit the excel solution
f(x) 1 1,5709 4 1,5727 1,5751 a. Complete the divided difference table for the data and costract the interpolating polynomial that uses all data. b. Using forward-divided differences , Find f(3,5)=? 3.

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Obtain the Lagrange interpolating polynomial using all the data points below: x 0.5 1.0 1.5 2.0 2.5 f(x) 0.8415 0.9093 0.1411 -0.7568 -0.9589