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Suppose experimental data are represented by a set of points in the plane. An interpolating polynomial for the data is a polynomial whose graph passes through every point. In scientific work, such a polynomial can be used, for example, to estimate values between the known data points. Another use is to create curves for graphical images on a computer screen. One method for finding an interpolating polynomial is to solve a system of linear equations. Find the interpolating polynomial p(t)= a +at+ a₂t² for the data (1,14), (2,18), (3,20). That is, find ag, a₁, and a2 such that the following is true. 80 +8₁ (1)+8₂(1)² = 14 ao+a, (2) + a₂ (2)² =- = 18 ao+a, (3)+ a₂ (3)2 =2 = 20 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The interpolating polynomial is p(t)= B. There are infinitely many possible interpolating polynomials,

Suppose experimental data are represented by a set of points in the plane. An interpolating polynomial for the data is a polynomial whose graph passes through every point. In scientific work, such a polynomial can be used, for example, to estimate values between the known data points. Another use is to create curves for graphical images on a computer screen. One method for finding an interpolating polynomial is to solve a system of linear equations. Find the interpolating polynomial p(t)= a +at+ a₂t² for the data (1,14), (2,18), (3,20). That is, find ag, a₁, and a2 such that the following is true. 80 +8₁ (1)+8₂(1)² = 14 ao+a, (2) + a₂ (2)² =- = 18 ao+a, (3)+ a₂ (3)2 =2 = 20 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The interpolating polynomial is p(t)= B. There are infinitely many possible interpolating polynomials,

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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Suppose experimental data are represented by a set of points in the plane. An interpolating polynomial for the data is a polynomial whose graph passes through every point. In scientific work, such a polynomial can be used, for example, to estimate values between the known data points. Another use is to create curves for graphical images on a computer screen. One method for finding an interpolating polynomial is to solve a system of linear equations. Find the interpolating polynomial p(t) = a +at+ a₂t² for the data (1,14), (2,18), (3,20). That is, find ao. a₁, and a₂ such that the following is true. 80 +8₁ (1) +8₂(1)² = 14 ao+a, (2) + a₂ (2)² =- = 18 ao+a, (3)+ a₂ (3)2 =2 = 20 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The interpolating polynomial is p(t)= B. There are infinitely many possible interpolating polynomials.
Transcribed Image Text:Suppose experimental data are represented by a set of points in the plane. An interpolating polynomial for the data is a polynomial whose graph passes through every point. In scientific work, such a polynomial can be used, for example, to estimate values between the known data points. Another use is to create curves for graphical images on a computer screen. One method for finding an interpolating polynomial is to solve a system of linear equations. Find the interpolating polynomial p(t) = a +at+ a₂t² for the data (1,14), (2,18), (3,20). That is, find ao. a₁, and a₂ such that the following is true. 80 +8₁ (1) +8₂(1)² = 14 ao+a, (2) + a₂ (2)² =- = 18 ao+a, (3)+ a₂ (3)2 =2 = 20 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The interpolating polynomial is p(t)= B. There are infinitely many possible interpolating polynomials.
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