97年 - 97 中原大學轉學生招生考試_理工群組二、化學群組二：微積分#124600

1.=_________

2.=_________

3. =_________

4.=_________

5. =_________

6. Assume that f(x) ∈ C ∀x ∈ R and that f(t) dt = ,then f(0) =_________

7. f(x)=ax³+bx²+cx+d that has a local maxima value of 3 at -2 and a local minima value of 0 at 1, then 9a+3b+c+3d=_________

8. Suppose g is the inverse function of a differentiable function f and let G(x) =. If f(3) = 2 and f'(3) =, then G'(2) =_________

9. If f(x, y, z) = , then =_________

10.=_________

二、計算題:
1. Find where Q is the region bounded by the x-axis, the curve y = x², and the line x =.

2. Find the points on the sphere x² + y² + z² = 36 that are closest to and farthest from the point (1, 2, 2).

3. Find the area of the region that lies inside the circle r=3sinθ and outside the cardioid r=1+sinθ.