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Unformatted text preview: Final Exam, Math 151A/3, Fall 2001, UCLA, 12/11/2001, 8am-11am NAME: STUDENT ID #: This is a closed-book and closed-note examination. Please show all you work. Partial credit will be given to partial answers. There are 8 problems of total 100 points. Time: 3 hours. SCORE: I II III IV V VI VII VIII Total - I Construct in 3 different ways the Lagrange interpolating polynomial for the following data: x f ( x ) = xe x x = 0 x 1 = 1 e x 2 = 2 2 e 2 Method 1: by the definition of the Lagrange polynomial. Method 2: by Nevilles method. Method 3: by Newtons interpolatory divided-difference formula. II For the data in problem I, write the error formula, and find an upper bound for the absolute error, for x = 0 . 5. III 1. Giving two points x and x + h , with h > 0, and a function f C 2 [ x , x + h ], derive an approximation to f ( x ), with error term.), with error term....
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