[考古] 清大92年8系聯招
1. Let V be the volume of the solid in the first octant that is inside the
cylinder x^2+y^2=1 and bounded below by the xy-plane and above by the plane
3x+2y+6z=6 Then V= ?
2. Suppose f(x)is a continuous,nonnegative function on [0,1] and,for n=
0,1,2,......., let An = ∫f(x)x^n dx (上限1 下限0)
(a) Prove that A2 ≦ A1 ≦ A2+ A0/4
(b) Prove that lim An = 0.
n→∞
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