96年 - 96 國立中山大學轉學生招生考試試題_應數系二年級：微積分#122158

科目：研究所、轉學考(插大)-微積分 | 年份：96年 | 選擇題數：0 | 申論題數：10

試卷資訊

所屬科目：研究所、轉學考(插大)-微積分

選擇題 (0)

申論題 (10)

1. Suppose that f(x) =. Find a closed form for = 1, 2, ....

2. A ladder 8 m long leans against a wall 4 m high. The lower end of the ladder is pulled away from the wall at a rate of 2 m/sec. How fast is the angle between the top of the ladder and the wall changing when the angle is 60° = π/3 radians?

3. Compute .

4. The base of a certain solid is the circular disk x² + y² ≤ 4 in the xy-plane. Each plane perpendicular to the *x*-axis cuts the solid in an equilateral triangle. Find the volume of the solid.

5. Compute .

6. Evaluate

7. Find the area inside the circle r = 5 sin θ and outside the limacon r = 2 + sinθ.

8. Evaluate , where a ＞ 0, a ≠ 1.

9. Evaluate

10. Find the volume of the solid bounded by xy-plane, the cylinder x² + y² = 4, and the paraboloid z = 2(x² + y²).