111年 - 111 國立臺北大學日間學士班轉學生招生考試_統計學系日間學士班二年級：微積分#116868

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. (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 of34.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 ft/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 :- S second.

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

申論題 (4)

1. Evaluate the integral dydx.

2. Use a linear approximation for values of the function f(x, y) = 2x² + 4y² near the points (1, 2) to approximate the value of f(1.2, 2.1).

3.Find lnxdx.

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