MATH 4650 Midterm: Math4650SampleExam2
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Fall 2017: let f (x) = (x 1)ex and take h = 0. 01. (a) calculate approximation to f (2. 3) using the two-point forward-di erence formula. Also, compute the actual error and an error bound for you approximation. (b) solve part (a) using the two-point backward-di erence formula: use the most accurate formula to determine approximations that will complete the following table. f (x) x. 18. 82091: suppose that n (h) is an approximation to m for every h > 0 and that. M = n (h) + k1h + k2h2 + k3h3 + . for some constants k1, k2, k3, . Use the values n (h), n ( h an o(h3) approximation to m . 9 ) to produce: find the constants c0, c1, and x1 so that the quadrature. 0 f (x) dx = c0f (0) + c1f (x1) has the highest possible degree of precision.
