111年 - [非官方正解]111 國立臺北大學_轉學生招生考試試題_統計學系二年級：微積分#117717

科目：研究所、轉學考(插大)-微積分 | 年份：111年 | 選擇題數：6 | 申論題數：4

試卷資訊

所屬科目：研究所、轉學考(插大)-微積分

選擇題 (6)

1. Find all critical points for the function f(x, y) = x3 - y3 + 33xy and classify each as a relative maximum, a relative minimum, or a saddle point. (A) fhas a saddle point at (11,-11) and a relative minimum at (0,0). (B) fhas a saddle point at (0,0) and a relative maximum at (11,-11). (C) fhas a saddle point at (0,0) and a relative minimum at (11,-11). (D) fhas a saddle point at (11,-11) and a relative maximum at (0,0).

2. Find the relative extrema of the function. Round your answer to one decimal place. 3m (A) Relative minimum is (0,0.3). (B) Relative minimum is (0,-0.3)； relative maximum is (1,0.3). (C) Relative minimum is (-1,-0.3)； relative maximum is (1,0.3). (D) Relative maximum is (0,0.3).
3. A bus company will charter a bus that holds 52 people to groups of 34 or more. If a group contains exactly 34 people, each person pays $65. In large groups, everybody's fare is reduced by $1 for each person in  excess 34. Determine the size of the group for which the bus company's revenue will be greatest. (A) 34 with revenue $2210. (B) Groups of 49 or 50 with revenue $2450. (C) Groups of 49 or 50 with revenue $2210. (D) 34 with revenue $2450.

4. Determine whetherexists. (A) does not exist. (B) (C)

5. Suppose a person standing at the top of a building 240 feet high throws a ball vertically upward with an initial velocity of 32 A/sec. When is the velocity 0? What is the significance of this time? Hint: Suppose the height of the ball above the ground at time t is H(t) = -16t2+ b t+c feet. (A) The ball is at its lowest point when t = 3 second. (B) The ball is at its lowest point when t = 2 second. (C) The ball is at its highest point when t = 1 second. (D) The ball is at its highest point when t= 5 second.

6. Choose the correct sketch of the indicated level curve f(x, y) = C for the given constant C. f(x,y) = 9yex； C=2.(A)(B)(C)(D)

申論題 (4)

1. Evaluate the integral 6564067f7a169.jpg. 
2. Use a linear approximation for values of the fiunction f(a, y) = 2x2 + 4y2near the points (1, 2) to approximate the value of f(1.2,2.1).

3. Find 656406f2ec42f.jpg lnxdx.

4. Find the volume of the solid obtained by rotating the region bounded by the graphs of 656406c563265.jpgand g(x) = x2 about the x-axis.