Suppose experimental data are represented by a set of points in the plane. An interpolating polynomial for the data is a polynomial whose grapl 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) = ao + aqt+ azt² for the data (1,10), (2,14), (3,20). That is, find a,, a1, and az such that the following is true. ao + a1(1) + az(1)? = 10 ao + a1 (2) + az(2)? = 14 ao + a1 (3) + az(3)² = 20 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The interpolating polynomial is p(t) = | O B. There are infinitely many possible interpolating polynomials. O c. There does not exist an interpolating polynomial for the given data.
Suppose experimental data are represented by a set of points in the plane. An interpolating polynomial for the data is a polynomial whose grapl 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) = ao + aqt+ azt² for the data (1,10), (2,14), (3,20). That is, find a,, a1, and az such that the following is true. ao + a1(1) + az(1)? = 10 ao + a1 (2) + az(2)? = 14 ao + a1 (3) + az(3)² = 20 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. O A. The interpolating polynomial is p(t) = | O B. There are infinitely many possible interpolating polynomials. O c. There does not exist an interpolating polynomial for the given data.
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 of (SEE PICTURE)
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) = ao + aqt+ azt for the data (1,10), (2,14), (3,20). That is, find ag, a1, and az
such that the following is true.
ao + a1(1) + az(1)2 = 10
ao + a1 (2) + az(2)² = 14
= 20
ao + a1 (3) + az(3)2 =
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.
c. There does not exist an interpolating polynomial for the given data.
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