※ 引述《spss520 (剩下一个月啦)》之铭言： : Let f[0,1]→R be continuous function and f(0)=0 : 1 : show lim ∫ f(x^n)dx=0 : n→∞ 0 : 谢谢大家 1 proof : lim ∫ f(x^n) dx n→∞ 0 1 = ∫ lim f(x^n) dx 0 n→∞ 1 = ∫ f(lim x^n) dx --------------(1) 0 n→∞ Since f(lim x^n) n→∞ = f(x) = f(0) = 0 , 0 ≦ x < 1 f(1) , x = 1 1 , (1) => lim ∫ f(x^n) dx n→∞ 0 1 = ∫ f(lim x^n) dx 0 n→∞ 1 = ∫ f(0) dx 0 1 = ∫ 0 dx = 0 0 --

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