Su95ex2 - and(2 e 2 Express the coefficients b i i=0,1,2,3...

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Su 95 EGN 3420 EXAM 2 Name __________________ DO ANY 4 PROBLEMS Problem 1 (25 pts) Grade: Y___, N___ The following data points are to be approximated by a straight line: x i 0 1 1 2 3 y i 0 1 2 3 3 A) Find the equation of the Least Squares regression line thru the data points. B) Using the line y = x (not the Least Squares line) for interpolation, find the coeficient of determination r 2 .
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Su 95 EGN 3420 EXAM 2 Name__________________________ Problem 2 (25 pts) Grade: Y___, N___ For the system of equations below: x + y - 2z = 0 2x + ky + z = -3 x - 2y + z = 0 A) Find the value of k for which the equations do not have a unique solution. B) Use the Gauss-Jordan Elimination Method, starting with the augmented matrix (A|b) to find the solution when k=0.
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Su 95 EGN 3420 EXAM 2 Name__________________________ Problem 3 (25 pts) Grade: Y___, N___ Estimate the function f(x) = e x at x=1 by fitting a 3rd order Newton Divided Difference polynomial thru the four points: (0, e 0 ), (0.5, e 0.5 ), (1.5, e 1.5
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Unformatted text preview: ) and (2, e 2 ). Express the coefficients b i , i=0,1,2,3 to five places after the decimal point and use them to estimate f(1). Su 95 EGN 3420 EXAM 2 Name__________________________ Problem 4 (25 pts) Grade: Y___, N___ A Lagrange polynomial of order 3, i.e. f 3 (x), is needed to pass thru the points: (0,0), (1,1), (2,8), and (4,64). What is the value of f 3 (3)? Su 95 EGN 3420 EXAM 2 Name__________________________ Problem 5 (25 pts) Grade: Y___, N___ Use Trapezoidal Integration with n=5 intervals to estimate the definite integral 1 3 I x dx = ∫ Let the result be called I 5 . Repeat the process using m=10 intervals with I 10 as the result. Use the results for I 5 and I 10 to obtain an improved estimate of I, called I 5/10 . Round all intermediate and final calculations to 5 places after the decimal point. i x i f i = f(x i ) 1 2 3 4 5 6 7 8 9 10...
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This note was uploaded on 06/09/2011 for the course EGM 4320 taught by Professor Klee during the Spring '11 term at University of Central Florida.

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Su95ex2 - and(2 e 2 Express the coefficients b i i=0,1,2,3...

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