Given the distinct points xi, 2 = Yi, i 0,1, · " = ., n+1, and the points n+ 1, let q be the Lagrange polynomial of degree n for the set of points {(xi, yi): i 0, 1,..., n} and let r be the Lagrange polynomial of degree n for the points {(xi, Yi): i = 1, 2, ..., n +1}. Define = p(x) = = (x − xo)r(x) — (x − xn+1)q(x) Xn+1 - x0 Show that is the Lagrange polynomial of degree n + 1 for the points {(x, yi): i = 0, 1, ..., n +1}.
Given the distinct points xi, 2 = Yi, i 0,1, · " = ., n+1, and the points n+ 1, let q be the Lagrange polynomial of degree n for the set of points {(xi, yi): i 0, 1,..., n} and let r be the Lagrange polynomial of degree n for the points {(xi, Yi): i = 1, 2, ..., n +1}. Define = p(x) = = (x − xo)r(x) — (x − xn+1)q(x) Xn+1 - x0 Show that is the Lagrange polynomial of degree n + 1 for the points {(x, yi): i = 0, 1, ..., n +1}.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 22E
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