92年 - 92 中原大學轉學生入學招生考試_理工、化學、工學(進修部)群組二年級：微積分#124619

1. Consider the function definded by
f(x) =, f(x) =_______

2. Find =_______

3. Find =_______ , if

4.=_______

5.=_______

6. The point on the ellipse 4x² + 9y² = 36, that is nearest the origin is __________

7. The arc of the parabola y=x² form (1,1) to (2,4) is rotated about the y-axis. Then the area of the resulting surface is ________.

8. The area of the region that consists of all points that lie within the circle r=2cosθ but outside the circle r=1 is ________.

9. If u=, then =________.

10. =________.

二、計算題
1. Find the interval of convergence of the series .

2. Find the maximum and minimum values of f(x,y)=2x²+y²-4x-2y+5 on the closed set S=