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final151a.01f_short

final151a.01f_short - Final Exam Math 151A/3 Fall 2001 UCLA...

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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 ———————-
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I Construct in 3 different ways the Lagrange interpolating polynomial for the following data: x f ( x ) = xe x x 0 = 0 0 x 1 = 1 e x 2 = 2 2 e 2 Method 1: by the definition of the Lagrange polynomial. Method 2: by Neville’s method. Method 3: by Newton’s 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 0 and x 0 + h , with h > 0, and a function f C 2 [ x 0 , x 0 + h ], derive an approximation to f ( x 0 ), with error term.
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