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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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 Summer '08
 Kyung
 Statistics, Numerical Analysis, Derivative, Normal Distribution, probability density function, Cumulative distribution function, random numbers

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