100年 - 100 國立中山大學轉學生招生考試試題_應數系：微積分#121822

科目：研究所、轉學考(插大)-微積分 | 年份：100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. Find the limit: .

2. The edges of a cube are expanding at a rate of 8 centimeters per second. How fast is the surface area changing when each edge is 6.5 centimeters?

3. Prove that if f is differentiable on (-∞,∞) and f'(x) ＜ 1 for all real numbers, then f has at most one fixed point. A fixed point of a function f is a real number c such that f(c) = c.

4. Show that the function f(x) = is constant for x ＞ 0.

5. Find the area of the largest rectangle that can be inscribed under the curve in the first and second quadrants.

6. Sketch the graph of g(x) = and determine g'(0).

7. Find the radius and interval of convergence of

8. Find the Maclaurin series for the function g(x) =.

9. Show that any tangent plane to the cone

z² = a²x² + b²y²

passes through the origin.

10. Find the volume of the region of points (x, y, z, w) such that x² + y² + z² + w² ≤ a².