Sp99exF - x i y i = f x i 0.0 0.000 0.5-0.375 1.0 0.000 1.5...

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Sp 99 EGN 3420 FINAL Name_______________________ SHOW ALL WORK! Problem 1 (35 pts) Consider the definite integral I where =1.0 , = 2.0 and ( ) = = z f x dx a b f x a b x ( ) 1 2 , A) Fill in the table below with f ( x i ) rounded to 4 places after the decimal point. Find I 10 using Trapezoidal Integration with 10 intervals to approximate I. Express your answer to 4 places after the decimal point. i x i f ( x i ) 0 1.0 1 2 3 4 5 6 7 8 9 10 2.0 B) Find I 5 using Trapezoidal Integration with 5 intervals to approximate I. Express your answer to 4 places after the decimal point. C) Find I using the results of Parts A) and B) to obtain an estimate of I. Express your answer to 4 places after the decimal point. D) Find the truncation error in the estimate obtained in Part C). Express your answer to 4 places after the decimal point.
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Sp 99 EGN 3420 FINAL Name_______________________ SHOW ALL WORK! Problem 2 (35 pts) The following data points were obtained experimentally.
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Unformatted text preview: x i y i = f ( x i ) 0.0 0.000 0.5-0.375 1.0 0.000 1.5 1.875 2.0 6.000 2.5 13.125 3.0 24.000 3.5 39.275 4.0 60.000 4.5 86.625 5.0 120.00 A) Find the Normal Equations to solve for the coefficients of the Least Squares Quadratic through the data points. B) Solve for the coefficients and express the results to 3 places after the decimal point. C) Find SST D) Find r 2 if SSE = 96.525 E-) The unknown function f ( x ) = x 3 - x . Find the true relative error when using the Least Squares Quadratic for prediction at x = 3.25 Sp 99 EGN 3420 FINAL Name_______________________ SHOW ALL WORK! Problem 3 (30 pts) Given the following system of equations x x x x x x x K x x x x x Kx x 1 2 3 4 1 3 4 1 2 3 4 2 3 4 3 2 2 3 8 2 2 2 + +-=-+-=-+-= +-= Find the value(s) of K for which there exist an infinite number of solutions....
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