MAD4401 Test2 - x using the following points(a x − 2 h x...

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Name MAD 4401, Numerical Analysis Keesling Test 2 Due 10/21/11 Do all problems. Do all work in the space provided. Each problem is worth 10 points. Due at the beginning of class on Friday, Oct 21, 2011. 1. Assume a means of generating random numbers that are from the uniform distribution on [0,1]. Using this determine a means of generating random numbers from the cumulative distribution function 1 π arctan( x ) + 2 . 2. Determine a means for generating random numbers from the uniform distribution on the interval [ a , b ] given a means of generating random numbers from a uniform distribution on [0,1].
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3. Determine a means of generating random numbers from the set {1,2,3,4,5,6} given a means of generating a uniform distribution from a uniform distribution on [0,1] . This would simulate the outcome of rolling a single die. 4. Determine a formula for estimating the derivative of f at the point
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Unformatted text preview: x using the following points. (a) x − 2 h , x − h , x + 3 h , x + 4 h { } (b) x − h , x + h { } 5. For each of the above formulas, what is the error in the estimate of the derivative. Explain. 6. For each of the formulas in Problem 4, what is optimal h to be used in estimating the derivative. Explain. 7. Determine a formula for estimating the 3 rd deriviative of f at x using the following points. (a) x − 4 h , x − 2 h , x − h , x + 3 h , x + 4 h { } (b) x − 5 h , x − 2 h , x − h , x + 3 h , x + 5 h { } 8. What is the error in the estimate of the third derivative in each of the formulas above. 9. For each of the formulas in Problem 7, what is the optimal h to be used in estimating the third derivative. Explain. 10. For the points in Problem 7 find a formula for estimating the 4 th derivative....
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MAD4401 Test2 - x using the following points(a x − 2 h x...

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