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試卷名稱：114年 - 114 國立清華大學學士後醫學系單獨招生考試_學士後醫學系/智慧資訊科技組：資訊科學#135660
年份：114年
科目：學士後西醫◆資訊科學
40. Consider the continuous function f(x) = 3 cos 2x + 4 sin 2x, and let g(x) = a cos x + b sin x be a linear combination of the functions cos x and sin x.
Define inner product of two functions as (f, g) = 
f(x)g(x)dx. Please find a and b such that ||f - g||² = 
|f(x) – g(x)|² dx is minimized. Which of the following shows the correct answer?
(A) a = 4 and b = 3
(B) a = 3 and b = 4
(C) a = 0 and b = 0
(D) a = 3 and b = -4
(E) a = -3 and b = 4