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Quiz 25B Solution Guyang Cao December 9 2024 1 Question 1 Solution By the definition of f t in case 1 substitute t with 1 2 3 we have f 1 12 f 2 2 f 3 2 Since the error is 0 in this case by the formula of Simpson s integral we have e 3 1 6 f 1 4f 2 f 3 3 12 8 2 2 3 and 3 e 2 as desired 1 Similarly in case 2 we know f 1 f 2 f 3 0 so the result of Simpson s integral should be 0 by the formula so 4 and 5 are both 0 Moreover by the error formula of Simpson s method we have E f 4 c 2880 25 0 266 or 0 267 and therefore 1000 E 266 or 267 2880 b a 5 4 1
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