# Berkeley MATH 128A - Numerical Analysis Sample Midterm II (5 pages)

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**View the full content.**## Numerical Analysis Sample Midterm II

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## Numerical Analysis Sample Midterm II

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Problems/Exams

- Pages:
- 5
- School:
- University of California, Berkeley
- Course:
- Math 128a - Numerical Analysis

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Prof Ming Gu 861 Evans tel 2 3145 Email mgu math berkeley edu http www math berkeley edu mgu MA128A2008S Math128A Numerical Analysis Sample Midterm II This is a closed book closed notes exam You need to justify every one of your answers Completely correct answers given without justification will receive little credit Do as much as you can Partial solutions will get partial credit Look over the whole exam to find problems that you can do quickly You need not simplify your answers unless you are specifically asked to do so 1 10 Points Your Name Your SID Your GSI Problem Maximum Score 1 4 2 24 3 24 4 24 5 24 Total 100 Your Score Math128A Numerical Analysis Sample Midterm II 2 Boole s Rule for numerical integration on the interval a b is given by I4 x 2h 7f a 32f a h 12f a 2h 32f a 3h 7f b 45 a Show that the degree of precision of this formula is 5 b Develop the Composite Boole s Rule for integration on a b 2 Math128A Numerical Analysis Sample Midterm II 3 3 Construct the natural cubic spline that approximates f x at the nodes 1 0 1 sin x x Math128A Numerical Analysis Sample Midterm II 4 Suppose that L lim f h and L f h c6 h6 c9 h9 h 0 Find a combination of f h and f h 2 that is a much better estimate of L 4 Math128A Numerical Analysis Sample Midterm II 5 5 Given h 0 1 f 0 0 f 0 1 0 01 and f 0 2 0 04 find a second order approximation to f 0 0

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