2. (a) Find the unique polynomial of degree 2 or less such that f(0) = 1, f(1) = 3, f(3) = 55using(i) the Lagrange interpolation(ii) the Newton divided difference interpolation.(b) Find the values of y at z = 21 and 2 = 28 from the following data:x20232629y0.34200.3907 0.43840.4848

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Answered: 2. (a) Find the unique polynomial of…

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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8. Consider the functions f : (4, 0) → R where f(x) = sin x and g : (-12,3) → R where g(x) = |x + 5|. %3D (a) Find the rule for the function f o g. (b) Find the domain for the function f o g.
(a)Use the Lagrange Interpolation Formula to find a polynomial of the form f(x) = ar? + bx + cthat fits all the following values. -2 1 y = f(z) 14 17 105 Hence find: () a +b+c () f'(1) (i) f"(3)
Given a set of data points determine Newton's interpolation polynomial of higher degree which passes through these points f(x) 3
1. for f (x) = cosx + sinx function; (Table attached in to description) table is given. a) Find the Lagrange interpolation polynomial P2(x) interpolating the function f(x). b) Using this polynomial, calculate the values of f(pi / 12 = 0.2618) and P2(pi / 12 = 0.2618) with seven digits after the comma. c) Determine an error upper limit for R2(x).
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1. How do you find the linearization of f(x) at x = a? Illustrate with a concrete example
1. for f (x) = cosx + sinx function; (Table attached in to description) table is given. a) Find the Lagrange interpolation polynomial P2(x) interpolating the function f(x). b) Using this polynomial, calculate the values of f(pi / 12 = 0.2618) and P2(pi / 12 = 0.2618) with seven digits after the comma. c) Determine an error upper limit for R2(x).
3. Interpolation Compute fo) and f(3). Use Newton's, Lagrange's, Forward and Backward Gregory Newton's Methods x -1 1 2 4 5 f(x) 13 15 13 33 67
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2. (a) Find the unique polynomial of degree 2 or less such that f(0) = 1, f(1) = 3, f(3) = 55 using (i) the Lagrange interpolation (ii) the Newton divided difference interpolation.