103年 - 103 國立中山大學轉學生招生考試試題_光電工程學系：微積分#121892

科目：研究所、轉學考(插大)-微積分 | 年份：103年 | 選擇題數：0 | 申論題數：20

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 (20)

1. Find =__①__

2. Find = __②__ in terms of x and y if x²y² - 2x = 3.

3. Find all asymptotes = __③__ of f(x) =.

4. A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 14 cubic centimeters. Find the radius = __④__ of the cylinder that produces the minimum surface area.

5. Evaluate =__⑤__

6. Evaluate =__⑥__

7. Find the equation = __⑦__ of the tangent line to y = at (2, 1).

8. Find =__⑧__

9. Find the volume =__⑨__ of the solid generated by revolving the plane region bounded by the graphs of y = x² and y = 4x - x² about the line x = 4.

10. Find the volume =__⑩__ of the solid of revolution formed by revolving the circle x² + (y - 3)² = 4 about the x-axis.

11. Find =__⑪__

12. Evaluate =__⑫__

13. Determine the convergence or divergence of =__⑬__

14. Find the Maclaurin series =__⑭__ for the function f(x) = cos² x.

15. Find the arc length =__⑮__ of the curve x = a(θ - sin θ) and y = a(1 - cos θ) on the interval [0, 2π].

16. Find the area =__⑯__ of the triangle with the given vertices A(2, -3, 4), B(0, 1, 2), and C(-1, 2, 0).

17. Find the maximum value =__⑰__ of the directional derivative at (3, 2).

18. Find the minimum value =__⑱__ of f(x, y, z) = x² + y² + z² subject to constraints x + 2z = 6, x + y = 12, x ≥ 0, y ≥ 0, and z ≥ 0.

19. Evaluate =__⑲__

20. Find the volume =__⑳__ of the solid is inside the sphere x² + y² + z² = 4 and above the upper nappe of the cone z² = x² + y².