Midterm1_2008 - COT 3502 Computer Model Formulation Midterm Exam 1 February 14 2007 Closed books notes and computers Calculators should be used

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Computer Model Formulation Midterm Exam 1 February, 14, 2007 Closed books, notes, and computers. Calculators should be used only for arithmetic calculations (not for plotting or analytical derivations). 1. (20 points) Consider the following function. -4 -3 -2 -1 0 1 2 -20 -15 -10 -5 0 5 10 15 20 x y (a) Using this graph, perform 2 iterations of the bisection method. The initial interval has the following lower and upper boundaries: x l = -1 and x u = 2. Make sure to clearly label the plot! (b) Estimate the number ( n ) of the bisection method iterations needed to obtain an approximation x ( n ) r to the root x 0 with precision e n = | x ( n ) r - x 0 | < 10 - 6 . Assume that the initial interval is the same as in part (a). (c) Can a bracketing method converge to the root at x = - 2? Why or why not? (d) Consider the method of false position. If your initial interval is x l = - 4, x u = 2, to which of the two roots will the iterations converge? 1
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This note was uploaded on 02/07/2009 for the course COT 3502 taught by Professor Hawkins during the Spring '08 term at University of Florida.

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Midterm1_2008 - COT 3502 Computer Model Formulation Midterm Exam 1 February 14 2007 Closed books notes and computers Calculators should be used

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