Quiz 23B Solution Guyang Cao December 2 2024 1 Question 1 Solution Following the statement in the problem we get the Below Matlab code 1 and we get the optimal k value be 3 9960 which means the desired result is 3996 For another variation of the problem we get the result 4070 4069 and 4071 also allowed 2 Question 2 2 Solution For Rule 1 it s the standard Simpson s method within the interval 0 1 you can refer to p6 of Lecture Note 18 to check Therefore rule1 S1 For Rule 2 it can be seen as the Trapezoid method used twice respectively on 0 0 5 and 0 5 1 since the weight and the function value investigated can make the integral I2 f 0 f 0 5 f 0 5 f 1 1 4 1 4 Therefore rule2 T2 For Rule 3 it does not correspond to any rules among R M T S so we accept any answer among X X1 X2 X3 and X4 for rule3 For Rule 4 it can be seen as the midpoint method used three timws respectively on 0 1 2 3 1 since the weight and the function value investigated can make the integral 3 and 3 1 3 2 2 0 6 1 6 4 2 6 3 6 6 4 6 f 5 6 I4 f f Therefore rule4 M3 3
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