94年 - 學士後西醫微積分94微積分#84743

科目：微積分 | 年份：94年 | 選擇題數：26 | 申論題數：0

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所屬科目：微積分

選擇題 (26)

1. Given that x = r cosθ and y = r sinθ , then

2. If and then

3. If , then

4. If ∑ a_n does not converge, then ∑ │a_n│ does not converge.

5. If f ′ is continuous on R = (−∞,∞) and f(x) = 0 , then

6. If f is a differentiable real value function on (a,b) and c ∈ (a,b) such that f ′(c) = 0 ,then f has a relative maximum or minimum at c.

7. If f ′ is bounded , then f is bounded.

8. The

9. If a function f :[a,b] → R is continuous, then f is Riemann integrable.

10.

(A)O (B)X

11. If the interval of convergence for power series is (-2,2) , then the interval of convergence for power series is :

(A) (−√2, √2) (B) (−2, 2) (C) (0, 4) (D) (1− √2,1+ √2) (E) (−1,1)

12.

(A) 1/2 (B) √3 (C)

13. Find the arc length of the curve , 1 ≤ x ≤ 4 .

(A) 36 (B) 30/4 (C) 62/5 (D) 126/6 (E) 254/7

14. Find the derivative of the function f(x) = 2^-x sin x² .

(A) 2^-x+1x cos x² - 2^-x-1sin x²

(B) 2^-x+1x cos x² - 2^-xln 2sin x²

(C) 2^-x cos x² - 2^-x-1sin x²

(D) 2^-xx cos x² - 2^-x-1ln 10 sin x²

(E) 2^-x+1x cos x² - 2^-xsin x²

15.

(A) 3 (B) ln 3 − ln 2 (C) 2ln 2 (D) ln2−ln3 (E) 2ln 3

16. If f(x) = cos 2x , find the value of f⁽⁸⁾(0) .

(A) 128 (B) –128 (C) –256 (D) 256 (E) 512

17. The gamma function Γ(n) is defined by

(A) 0 (B) 1 (C) 2 (D) 3 (E) 4

18. Find the area of the region that lies inside both the curves r = 4sinθ and r = 4 cosθ . (A) 2π + 1 (B) 2π −1 (C) 2π + 4 (D) 2π − 4 (E) 2π

19. Find the terms of the Maclaurin series for , as far as the term in x³ .

(A) 1 - x + x² -x³

(B) 1 + x - 1/2 x² + 1/3 x³

(C) 1 - x + 3/2 x² - 5/2 x³

(D) 1 + x + 3x² + 5 x³

(E) 1 - x + 3/2 x² - 7/3 x³

20. Find the volume of the solid bounded below by the xy-plane and above by the paraboloid z = 1 ( x² + y²)

(A) π (B) π/2 (C) π/3 (D) π/4 (E) π/8

21. How many local maximum points in the following function:

(A) none (B) 1 (C) 2 (D) 3 (E) 4

22.

(A) 0 (B) 1/2 (C) π (D) π/2 (E) π/4

23. If , find F′(x) where x ≠ 0 .

24.

(A) 0 (B) π (C) π² (D) 2π³ (E) 4π³

25.

26. The maximum value of the function f (x, y, z) = x + 2y + 3z subject to the constraint x² + y² + z² = 25 is _______.

申論題 (0)