104年 - 104 東吳大學_暑假轉學生招生考試_經濟學系二年級：微積分#116012

1.= (A)(B)(C)(D) The limit does not exist. (E) None of these

2. Find the equation of the line tangent to the graph of  f(x)= at (2, 3) . (A)y=-4x+7 (B)y=4x+7 (C)y=2x+7 (D)y=-2x+7(E) None of these

3. For x²+y²=xy+7, use implicit differentiation to find . (A) (B) (C) (D)(E) None of these

4. Find all relative extrema of the function f(x)=. (A) Relative maximum:(B) Relative maximum: (C) Relative minimum: (D) Relative minimum:(E) None of these

5. Find all slant asymptotes of the function f(x)=. (A)y=2x-1 (B)y=2x+1 (C)y=2x (D) The function has no slant asymptote. (E) None of these

7. f(x)=log₂(x²-1)，then f'(2)= (A) (B) (C) (D) (E) (F) None of these

8. If f(x)=，then f'(2)= (A)64(1+ln 2) (B)32(1+ln 2) (C)16(1+ln 2) (D)8(1+ln 2) (E) None of these

9. Suppose F(x) is an antiderivative of  and F(0) = 1. What is F(9)? (A) 1 (B) 2 (C) (D) 19 (E) 21 (F) None of these

10.=(A) (B) (C) (D) (E) None of these

11.= (A) (B) (C) (D) (E) None of these

12. Find the average value of f(x)= from x =0 to x = 3. This answer is (A) (B) (C) (D) (E) None of these

14.= (A) (B) (C) (D)(E) None of these

15.=(A) (B) (C) (D) (E) None of these

16. Find the relative extrema and saddle points of the function f(x,y)=. (A) Relative maximum at   Saddle point at (0, 0, 0). (B) Relative minimum at   Saddle point at (0, 0, 0). (C) Relative maximum at (0, 0, 0). Saddle point at  (D) Relative minimum at (0, 0, 0). Saddle point at  (E) None of these

17. Find the minimum value of f (x, y, z, w) = x²+y²+z²+w² subject to the constraint 3x+2y-4z+w-3=0. This answer is (A) (B) (C) (D) (E) None of these

18.=(A) (B) (C) (D) (E) None of these

19. Let f(t)=t²sect. What is? (A)(B) (C)(D)(E) None of these

20. Find the radius of convergence for the series . (A)0 (B)1 (C)2 (D)∞ (E)None of these