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Consider the polynomials A+ Bx+Cx². Note that the parabola W₁ = 2 (x² + x) equals one at x = 1 and zero at x = 0 and x = -1. Find the parabolas W2, W3, and y(x): (a) w2 equals one at x = 0 and zero at x = 1 and x = -1. (b) w3 equals one at x = -1 and zero at x = 0 and x = 1. (c) y(x) equals 4 at x = 1 and 5 at x = 0 and 6 at x = -1. Express your answer in terms of W1, W2, W3.

Consider the polynomials A+ Bx+Cx². Note that the parabola W₁ = 2 (x² + x) equals one at x = 1 and zero at x = 0 and x = -1. Find the parabolas W2, W3, and y(x): (a) w2 equals one at x = 0 and zero at x = 1 and x = -1. (b) w3 equals one at x = -1 and zero at x = 0 and x = 1. (c) y(x) equals 4 at x = 1 and 5 at x = 0 and 6 at x = -1. Express your answer in terms of W1, W2, W3.

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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Consider the polynomials A+ Bx +Cx². Note that the parabola W₁ 1 and zero at x = 0 and x = -1. Find the parabolas W2, W3, and y(x): (a) w₂ equals one at x = 0 and zero at x = 1 and x -1. == (b) W3 equals one at x = -1 and zero at x = 0 and x = = 1. (x² + x) equals one at x = (c) y(x) equals 4 at x = 1 and 5 at x = 0 and 6 at x = -1. Express your answer in terms of W1, W2, W3.
Transcribed Image Text:Consider the polynomials A+ Bx +Cx². Note that the parabola W₁ 1 and zero at x = 0 and x = -1. Find the parabolas W2, W3, and y(x): (a) w₂ equals one at x = 0 and zero at x = 1 and x -1. == (b) W3 equals one at x = -1 and zero at x = 0 and x = = 1. (x² + x) equals one at x = (c) y(x) equals 4 at x = 1 and 5 at x = 0 and 6 at x = -1. Express your answer in terms of W1, W2, W3.
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