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# Fa96ex1 - e A 1 0.0000 1.5000 2 3 Bisection Method...

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EGN 3420 EXAM I Name________________________ Fa 96 SHOW ALL WORK! Problem 1 (25 pts) Consider the function f(x) = e x + x 2 . A third order truncated Taylor Series of f(x) expanded about the point x 0 = a and evaluated at the point x=2a is given below. f 3 (2a) = e a ( α 0 + α 1 a + α 2 a 2 + α 3 a 3 ) + β a 2 A) Find α 0 , α 1 , α 2 , α 3 , and β . B) For a = 0.1, find the truncation error E T = f(0.2) - f 3 (0.2) to 6 places after the decimal point. Work Area ……………………………………………………………………………………………… Ans. α 0 = _____, α 1 = _____, α 2 = _____, α 3 = _____, β = _____ E T = __________

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EGN 3420 EXAM I Name________________________ Fa 96 SHOW ALL WORK! Problem 2 (30 pts) The function f(x) = x 4 - 5x 2 + 4 has a root located between 0 and 1.5. Fill in the tables below for the first three iterations of the Bisection Method and the False Position method. Express all answers to four digits after the decimal point. Iteration x l x u x r f(x l ) f(x r

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Unformatted text preview: ) e A 1 0.0000 1.5000 2 3 Bisection Method Iteration x l x u x r f(x l ) f(x u ) f(x r ) e A 1 0.0000 1.5000 2 3 False Position Method EGN 3420 EXAM I Name________________________ Fa 96 SHOW ALL WORK! Problem 3 (20 pts) Use the one point iteration method to locate the smaller root of the quadratic f(x) = x 2- 10x + 1. Choose g(x) = (x 2 +1)/10. Stop when the magnitude of the true error, E T falls below 0.00001 i x i x i+1 = g(x i ) E T = True root - x i 5.00000 1 2 3 4 5 6 7 8 EGN 3420 EXAM I Name________________________ Fa 96 SHOW ALL WORK! Problem 4 (25 pts) Find the matrix inverse A-1 to solve the system of equations Ax = b given below. x + y + z = 6 x-2y + z = 4x + y-2z = Work Area ……………………………………………………………………………………………… Ans. A-1 = , x = _____, y = _____, z = _____...
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