AUBG, Fall 2009, MAT 214 “Numerical Analysis” Second Quiz Variant 26 Name: ID#: Instructions: You can do as many problems as you like. A total of ten points is required for full credit. All collected points will be added to your total score for the course. Please, attach all calculations! Only well justiﬁed solutions will receive full credit. Problem 1 (Composite Simpson’s Rule) . Determine the values of n and h required to approximate [3 points] Z 14 . 5 13 . 5 x 3 ln x dx to within 10-5 by the Composite Simpson’s Rule, compute the approximation, and compare with the actual value. To ﬁnd the actual value, use the indeﬁnite integral Z x 3 ln x dx = x 4 ± ln x 4-1 16 ² + C. Problem 2 (Simpson’s Double Integral) . Use Simpson’s Double Integral with n = 3, m = 3 to [3 points] approximate Z 14 . 5 13 . 5 Z 16 . 5 x 15 . 5 x x y dy dx and compare the result with the actual value (which is very easy to compute). Problem 3
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