pracfinal - Math 104A Practice Final Do all the problems...

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Math 104A Practice Final Do all the problems and show all your work. 1. Let f (0 . 1) = 1 . 10517, f (0 . 2) = 1 . 22140, and f (0 . 3) = 1 . 34986. a) Find a first order approxi- mation to f 0 (0 . 2). b) Find a second order approximation to f 0 (0 . 2). 2. Suppose that N ( h ) is an approximation to M for every h > 0 and that M = N ( h ) + K 1 h + K 2 h 2 + K 3 h 3 + ··· for some constants K 1 , K 2 , K 3 , . . . . Use the values N ( h ), N ( h 3 ), and N ( h 9 ) to produce and O ( h 3 ) approximation to M . 3. The (simple) trapezoidal rule applied to R 4 0 f ( x ) dx gives the value 2 and Simpson’s rule gives the value 1. What is f (2)? 4. Derive a quadrature formula for approximating Z 3 0 f ( x ) dx in terms of f (0), f (1), f (2) and f (3). 5. a) Define the degree of accuracy or precision of a quadrature formula. b) What’s the degree of accuracy for the Composite Trapezoidal rule? c) What’s the degree of accuracy for the Composite Simpson’s rule? 6. Consider the integral
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This note was uploaded on 05/01/2009 for the course PSTAT 120A taught by Professor Mackgalloway during the Spring '08 term at UCSB.

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pracfinal - Math 104A Practice Final Do all the problems...

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