101年 - 101 國立中山大學轉學生招生考試試題_應數系：微積分#122157

科目：研究所、轉學考(插大)-微積分 | 年份：101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 dy/dx = __①__ given that y³ + y² - 5y - x² = -4.

2. Find the extrema = __②__ of f(x) = x³ - on the interval [-1, 2].

3. Find two positive numbers = __③__ which satisfy that the second number is the reciprocal of the first number and the sum is a minimum.

4. Evaluate = __④__

5. Evaluate ∫sec(1-x)tan(1-x)dx = __⑤__

6. Find = __⑥__ where f(x) = x³ - 1 and a = 26.

7. Find the volume = __⑦__ of the solid generated by revolving the region bounded by the graphs of y =, y = 0, x = 0, and x = 4 about the x-axis.

8. Find the area = __⑧__ of the surface generated by revolving y = , 0 ≤ x ≤ 6 about the x-axis.

9. Evaluate = __⑨__

10. Evaluate = __⑩__

11. Determine the convergence or divergence = __⑪__ of the series .

12. Find the interval = __⑫__ of convergence of the power series , k ＞ 0.

13. Find the Maclaurin series = __⑬__ for the function f(x) =.

14. Find the arc length = __⑭__ of the curve x = t² and y = 2t, 0 ≤ t ≤ 2.

15. Find the area = __⑮__ of the common interior of r = 4 sin 2θ and r = 2.

16. Determine whether the statement is true or false = __⑯__ . Every two lines in space are either intersecting or parallel.

17. Find the directional derivative = __⑰__ of f(x,y) = x² + 3y² at P(1,1) in the direction of Q(4, 5).

18. Find the minimum value = __⑱__ of f(x, y) = 3x + y + 10 subject to the constraint x²y = 6.

19. Evaluate = __⑲__

20. Find the volume = __⑳__ of the solid inside both x² + y² + z² = a² and (x - a/2)² + y² = (a/2)².