107年 - 107 台灣聯合大學系統(清華、交通、陽明、中央四校聯招)學士班轉學生考試_A3、A4、A7：微積分#112635

1. Find the critical number of y = .
Answer:________

2. Determine the limits of integration where a ≤ b such thatdx has minimal
  value. Answer:________

3. Evaluate dx. Answer:_______

5. Find the surface area of the portion of the plane z = 4 - 2x - 2y that lies above the circlex²+y²≤1 in the first quadrant. Answer :__________

7. Evaluate the integraldxdy.
Answer:___________

8. Use a change of variables to find the volume of the solid region lying below the surface and above the plane region R : region bounded by the parallelogram with vertices (0,0),(1,1), (5,0) and (4, -1): Answer:____________

b. (6分)

3. Find the maximum value of dy, where C is any circle in the xy-plane, oriented counterclockwise.