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PLEASE ANSWER 2 MAPLE MATLAB Interpolating Polynomials Text Reference: Section 1.2, p. 26 The purpose of this set of exercises is to show how to use a system of linear equations to fit a polynomial through a set of points. This exercise set expands ideas begun in Exercises 33 and 34 of Section 1.2, and applies these ideas to real data. Recall from the text that an interpolating polynomial for a set of points in the plane is a polynomial whose graph passes through each of the points. In general, it can be shown that given n points with no two points having the same first coordinate, there exists an interpolating polynomial p(t) = ao + at + at2 +... + an-1tn-1 of degree n - 1 or less. (See Exercise 11 in the Chapter 2 Supplementary Exercises for a proof of this fact.) Each of the n points determines a linear equation that the (unknown) coefficients ao, a1, 2, . .. , a,-1 in the polynomial must satisfy. Questions: 1. Find the interpolating polynomial of degree 3 which passes through (1,29), (1, -35), 2,31,and-3,-19. 2. To construct a fourth degree polynomial which "looks like" the graph of 2t, one could specify that the polynomial go through the following five points: (1, .5) , (0, 1) , (1, 2) , (2, 4), and (3,8). a) Find the desired interpolating polynomial. b) Use your technology to graph the interpolating polynomial on the same graph with y = 2t. How close are the values of the polynomial and the function for t values between -1 and 3? What happens when the polynomial is compared to the function at t values outside of this interval? If you needed to use the interpolating polynomial to approximate y = 2 what types of mathematical precautions would you take?

          PLEASE ANSWER 2
MAPLE
MATLAB
Interpolating Polynomials
Text Reference: Section 1.2, p. 26
The purpose of this set of exercises is to show how to use a system of linear equations to fit a polynomial through a set of points. This exercise set expands ideas begun in Exercises 33 and 34 of Section 1.2, and applies these ideas to real data.
Recall from the text that an interpolating polynomial for a set of points in the plane is a polynomial whose graph passes through each of the points. In general, it can be shown that given n points with no two points having the same first coordinate, there exists an interpolating polynomial p(t) = ao + at + at2 +... + an-1tn-1 of degree n - 1 or less. (See Exercise 11 in the Chapter 2 Supplementary Exercises for a proof of this fact.) Each of the n points determines a linear equation that the (unknown) coefficients ao, a1, 2, . .. , a,-1 in the polynomial must satisfy.
Questions:
1. Find the interpolating polynomial of degree 3 which passes through (1,29), (1, -35), 2,31,and-3,-19.
2. To construct a fourth degree polynomial which "looks like" the graph of 2t, one could specify that the polynomial go through the following five points: (1, .5) , (0, 1) , (1, 2) , (2, 4), and (3,8).
a) Find the desired interpolating polynomial. b) Use your technology to graph the interpolating polynomial on the same graph with y = 2t. How close are the values of the polynomial and the function for t values between -1 and 3? What happens when the polynomial is compared to the function at t values outside of this interval? If you needed to use the interpolating polynomial to approximate y = 2 what types of mathematical precautions would you take?

please answer 2 maple matlab interpolating polynomials text reference section 12 p 26 the purpose of this set of exercises is to show how to use a system of linear equations to fit a polynom 38655

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