Problem 1E: Use Lagrange interpolation to find a polynomial that passes through the points. a. (0,1),(2,3),(3,0)... Problem 2E: Use Newtons divided differences to find the interpolating polynomials of the points in Exercise 1,... Problem 3E: How many degree d polynomials pass through the four points (1,3),(1,1),(2,3),(3,7) ? Write one down... Problem 4E: (a) Find a polynomial P(x) of degree 3 or less whose graph passes through the points (0,0), (1,1),... Problem 5E: (a) Find a polynomial P(x) of degree 3 or less whose graph passes through the four data points... Problem 6E: Write down a polynomial of degree exactly 5 that interpolates the four points (1,1), (2,3), (3,3),... Problem 7E: Find P(0), where P(x) is the degree 10 polynomial that zero at x=1,...,10 and satisfies P(12)=44. Problem 8E: Let P(x) be the degree 9 polynomial that takes the value 112 at x=1, takes the value 2 at x=10, and... Problem 9E: Give an example of the following, or explain why no such example exists. (a) A degree 6 polynomial... Problem 10E: Let P(x) be the degree 5 polynomial that takes the value 10 at x=1,2,3,4,5 and the value 15 at x=6 .... Problem 11E: Let P1, P2, P3, and P4 be four different points lying on a parabola y=ax2+bx+c . How many cubic... Problem 12E: Can a degree 3 polynomial intersect a degree 4 polynomial in exactly five points? Explain. Problem 13E: Let P(x) be the degree 10 polynomial through the 11 points (5,5), (4,5), (3,5), (2,5), (1,5), (0,5),... Problem 14E: Write down 4 noncollinear points (1,y1), (2,y2), (3,y3), (4,y4) that do not lie on any polynomial... Problem 15E: Write down the degree 25 polynomial that passes through the points (1,1),(2,2),...,(25,25) and has... Problem 16E: List all degree 42 polynomials that pass through the eleven points (5,5),(4,4),...,(4,4),(5,5) and... Problem 17E: The estimated mean atmospheric concentration of carbon dioxide in earths atmosphere is given in the... Problem 18E Problem 1CP: Apply the following world population figures to estimate the 1980 population, using (a) the straight... Problem 2CP: Write a version of Program 3.2 that is a MATLAB function, whose inputs x and y are equal length... Problem 3CP: Write a MATLAB function polyinterp.m that takes as input a set of (x,y) interpolating points and... Problem 4CP: Remodel the sin1 calculator key in Program 3.3 to build cos1, a cosine key that follows the same... Problem 5CP: (a) Use the addition formulas for sin and cos to prove that tan(/2x)=1/tanx . (b) Show that (0,/4)... format_list_bulleted
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