103年 - 103 國立中山大學轉學生招生考試試題_物理系：微積分#121894

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 x² + y² = 36.

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

4. The sum of the perimeters of an equilateral triangle and a square is 10. Find the dimensions = __④__ of the triangle and the square that produce a minimum total area.

5. Evaluate = __⑤__

6. Find = __⑥__

7. Find the equation = __⑦__ of the tangent line to y = at (-2, 4).

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 = 2.

10. Find the volume __⑩__ of the solid of revolution formed by revolving the circle (x - 5)² + y² = 16 about the y-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) = 2 cosh x.

15. Find the arc length __⑮__ of the curve x = a cos³ θ and y = a sin³ θ on the interval [0, 2π].

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

17. Find the maximum value = __⑰__ of the directional derivative of w = xy²z² at P(2, 1, 1).

18. Find the maximum = __⑱__ of f(x, y, z) = xyz subject to constraints x + y + z = 32, x - y + z = 0, x ≥ 0, y ≥ 0, and z ≥ 0.

xy dy dx =__⑲__

20. Find the volume __⑳__ of the solid is bounded by r² + z² = a² and r = a cos θ.