※ 引述《likekeys (安口)》之铭言： : 虽然我查了一下之前有人回过这两个问题 : 但是还是想再讨论一下 : http://www.lib.ntu.edu.tw/exam/undergra/88/88035.htm : 试卷末的 乙丙 两题 : 乙题毫无头绪,用mean value 也不知怎令f (1) prove sin x < x let f(x)=x-sin x, f'(x)=1-cos x Since cos x < 1, f'(x)=1-cos x > 0 Hence, f(x)>f(0)=0, x-sin x > 0 sin x < x for 0 < x < π/2. (2) prove 2x/π < sin x let f(x) = sin x -2x/π f'(x) = cos x -2/π f''(x) = -sin x It's obviously that f''(x) < 0 for x in (0,π/2) That is, there is no local minimum in [0, π/2] local minimum occurs at x=0 or x=π/2 Since f(0)=0 and f(π/2)=0, so we know f(x)>f(0), sin x -2x/π>0 Hence, sin x > 2x/π for 0 < x < π/2. By (1) and (2), 2x/π < sin x < x for 0 < x < π/2. : 丙题我试想说它应该是希望完整一点的比较 : 所以我用二项展开式 推误差 : 我只能确定10-1/150比10-1/200的误差小 : 但是不知怎麽解释10-1/150比10-1/100误差小 : 想请问大家的想法 : 谢谢 --

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