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(10) 3 f(-1) = 1, f(1) = f(0) = 4, and f(r2) = f(1) = 1, to construct interpolating polynomials of legrees at most one and two. Then, use both resulting polynomials to approximate f(-0.5) and find tion

(10) 3 f(-1) = 1, f(1) = f(0) = 4, and f(r2) = f(1) = 1, to construct interpolating polynomials of legrees at most one and two. Then, use both resulting polynomials to approximate f(-0.5) and find tion

Advanced Engineering Mathematics
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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Given f(r) = x* – 4x² + 4, use the nodes 1o = –1, x1 = 0, and x2 = 1, and values f(ro) = f(-1) = 1, f(x1) = f(0) = 4, and f(x2) = f(1) = 1, to construct interpolating polynomials of degrees at most one and two. Then, use both resulting polynomials to approximate f(-0.5) and find the actual error of each approximation of f(-0.5). %3D
Transcribed Image Text:Given f(r) = x* – 4x² + 4, use the nodes 1o = –1, x1 = 0, and x2 = 1, and values f(ro) = f(-1) = 1, f(x1) = f(0) = 4, and f(x2) = f(1) = 1, to construct interpolating polynomials of degrees at most one and two. Then, use both resulting polynomials to approximate f(-0.5) and find the actual error of each approximation of f(-0.5). %3D
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