Q1a)Determine the Lagrange form of the interpolating polynomial P(x) that interpolates a function f(x) at x = 0, h and 3h, where h > 0. (Multiply the linear factors together, but leave P(x) as a sum of 3 quadratics in the variable x.) DELIVERABLES: All your work in constructing the polynomial.b) Derive the quadrature formula of the form a0f(0) + a1f(h) + a2f(3h) for approximating I = R 3h 0 f(x)dx that results from approximating the integral I by I ≈ R 3h 0 P(x)dx.Note: if you know only 3 function values of f(x) and they are at 3 unequally-spaced points 0, h and 3h, then this kind of quadrature formula can be used to approximate I. DELIVERABLES: All your work in deriving the quadrature formula. (a) (2 points) Determine the Lagrange form of the interpolating polynomial P(x) thatinterpolates a function f(x) at x = 0, h and 3h, where h> 0. (Multiply the linearfactors together, but leave P(x) as a sum of 3 quadratics in the variable x.)All your work in constructing the polynomial.DELIVERABLES:(b) (4 points) Derive the quadrature formula of the formaof (0) + a₁f(h) + a₂f (3h)for approximating I = f3h f(x)dx that results from approximating the integral I byI≈ f3h P(x) dx.00Note: if you know only 3 function values of f(x) and they are at 3 unequally-spacedpoints 0, h and 3h, then this kind of quadrature formula can be used to approximateI.DELIVERABLES: All your work in deriving the quadrature formula.

Answered: 0. (Multiply the linear factors…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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a)Determine the Lagrange form of the interpolating polynomial P(x) that interpolates a function f(x) at x = 0, h and 3h, where h > 0. (Multiply the linear factors together, but leave P(x) as a sum of 3 quadratics in the variable x.) DELIVERABLES: All your work in constructing the polynomial.

b) Derive the quadrature formula of the form a0f(0) + a1f(h) + a2f(3h) for approximating I = R 3h 0 f(x)dx that results from approximating the integral I by I ≈ R 3h 0 P(x)dx.

Note: if you know only 3 function values of f(x) and they are at 3 unequally-spaced points 0, h and 3h, then this kind of quadrature formula can be used to approximate I. DELIVERABLES: All your work in deriving the quadrature formula.

(a) (2 points) Determine the Lagrange form of the interpolating polynomial P(x) that
interpolates a function f(x) at x = 0, h and 3h, where h> 0. (Multiply the linear
factors together, but leave P(x) as a sum of 3 quadratics in the variable x.)
All your work in constructing the polynomial.
DELIVERABLES:
(b) (4 points) Derive the quadrature formula of the form
aof (0) + a₁f(h) + a₂f (3h)
for approximating I = f3h f(x)dx that results from approximating the integral I by
I≈ f3h P(x) dx.
0
0
Note: if you know only 3 function values of f(x) and they are at 3 unequally-spaced
points 0, h and 3h, then this kind of quadrature formula can be used to approximate
I.
DELIVERABLES: All your work in deriving the quadrature formula.

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