3 c Let f(x) = -x cos (2r) + x?, ro = 0, 1 = 0.3, x2 = 0.7.(a) Find Lagrange interpolating polynomial for f(r) using the three given nodes.(b) Using the nodes ro and æ1, construct the Hermite interpolating polynomial H3(x)for f(x) using the Lagrange coefficient polynomials.(c) Determine the natural cubic spline that interpolates the dataf(0) = 2, f(3) = 3, f(8) = 1%3D%3Dand find the approximate value of f(1.2).1(d) The cubic Legendre polynomial is P2(x) =(5.r -3r). Prove that it is orthog-%3Donal (over [-1, 1)) to all polynomials of degree 2.

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Answered: (c) Determine the natural cubic spline…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section: Chapter Questions

Problem 14T

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(c) Determine the natural cubic spline that interpolates the data S(0) = 2, f(3) = 3, f(8) = 1 and find the approximate value of f(1.2). 1. (A) Th