3b Let f(x) = x cos (2x) – a, xo = 0, 1 = 0.3,X2 = 0.7.(a) Find Lagrange interpolating polynomial for f(x) using the three given nodesleaving all coefficients correct to 5 decimal points.(b) Using the nodes r, and a1, construct the Hermite interpolating polynomial H3(r)for f(x) using the Lagrange coefficient polynomials expressing all coefficientscorrect to 5 decimal places.(c) Determine the natural cubic spline that interpolates the dataf(0) = 1, f(3) = 2, f(8) = 3and find the approximate value of f(3.2) correct to four decimal places.(d) The cubic Legendre polynomial is P2(x) = (5x³ – 3r). Prove that it is orthog-onal (over [-1, 1]) to all polynomials of degree 2.%3D

Solution a: Given function is f(x)=xcos(2x), x0=0, x1=0.3, x2=0.7 So table is x f(x) 0 0 0.3…

Answered: Let f(x) = x cos (2x) -², xo=0, x₁=0.3,…

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter4: Polynomial And Rational Functions

Section4.5: Rational Functions

Problem 54E

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Let f(x) = x cos (2x) -², xo=0, x₁=0.3, 22 = 0.7. (a) Find Lagrange interpolating polynomial for f(x) using the three given nodes leaving all coefficients correct to 5 decimal points.