98年 - 98 中原大學轉學生招生考試_理工群組二、 化學群組二、 資工二：微積分#124593

1. =_________

2.=_________

3. If f(x) =, for x ＞ 1, then f'(e) =_________

4. If f(x) =dt, for x , then =_________

5.=_________

6.=_________

7. =_________

8. If f(x,y) = , for x ＞0 and y , then =_________

9. The equation for the tangent plane to the surface x² + 4y² + 9z² = 3 at the point is ________.

10. The shortest distance between the parabola y = x² and the point (6, 3) is ________.

1. Define f(x, y) = for x, y . Show that f is not differentiable at (0,0).

2. Let f(x) =
Show that f is differentiable at each x and that f' is not continuous at 0.

3. Two right circular cylinders of radius 1 have axes that intersect at right angles. Find the volume of the solid common to the two cylinders.