5.Use appropriate Lagrange interpolating polynomials of degrees one, two, and three to approximateeach 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) = 18.82091b. f (-) if f(-0.75) = -0.07181250, f(-0.5) = -0.02475000, f(-0.25) = 0.33493750,f (0) = 1.10100000f (0.25) if f(0.1)а.= 0.62049958, f(0.2) = -0.28398668, f(0.3) = 0.00660095, f(0.4) =с.0.24842440d.f (0.9) if f(0.6) = -0.17694460, f(0.7) = 0.01375227, f(0.8) = 0.22363362, f(1.0) =0.658091977.The data for Exercise 5 were generated using the following functions. Use the error formula to find abound for the error, and compare the bound to the actual error for the cases n = 1 and n 2.f(x) = x In xf (x) = x + 4.001lx? + 4.002r + 1.101f(x) = x cos x - 2r2 +3x - 1а.b.с.d.f(x) = sin(e - 2)

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Answered: 5. Use appropriate Lagrange…

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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a. Find the linear approximating polynomial for the following function centered at the given point a.
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?
Differentiate the following functions D f(x) = x²-1 2²71
Let y = x3 + x2 + A . Construct a difference table from x= 0,1,2,3, and 4. Calculate y for x=4.5 by using Newton Interpolation Polynomial Formula. Also compare your results. (where ? given in the instructions) A=7
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Develop a program in a language of your choice to implement Newton or Lagrange interpolation polynomials. Use this program to calculate f(2.5) and f(4) employing the data given in question-2.
. 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
Compute the divided-differece table for the tabulated function. Write down the Newton polynomial P4(x). Evaluate P4(x) at x=2.5 and x=3.5. The underlying function for the data is f(x)=3.6/x. Compare the function values x=2.5 and x=3.5 with the actual function values (calculate the percent true error).
given that the instantaneous rate of change of a polynomial is never zero on the entire domain of the function, what can you state about the function’s behaviour?
The observed values of a function f (x)at the four positions of the independent variable x are as follows: 3 6. f(x) 707 819 866 966 Using Lagrange's interpolation formula, find the best estimate for the value of the function at the position 4 of the independent variable.
A. Find the coefficients of the following derivative fi" = C₁-1fi-1 + Cifi + C₁+1f1+1 C

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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.