[考古] 請教兩題微積分

[ADAH33 (逐漸消失的生命)]

 1. Let f(x) be a cont function on [1,a]

   1 < = f(x) < = a  for all x 屬於 [1,a]

   prove that there exists one number k 屬於 (1,a)

   such that kf(k)=a

 2. let G(t)=   積分     e^(-x)x^(t-1) dx
             0到 無窮大
    (1) show that G(n)=(n-1)! (2) find G(1/2)

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