91年 - 91 國立臺灣師範大學_學士班轉學生招生考試試題_資訊教育學系二年級：微積分#122376

科目：研究所、轉學考(插大)-微積分 | 年份：91年 | 選擇題數：0 | 申論題數：8

試卷資訊

所屬科目：研究所、轉學考(插大)-微積分

選擇題 (0)

申論題 (8)

1. (15 pts) An oil can is to be made in the form of a right circular cylinder, as illustrated in Fig. 1, to contain V m³ of oil. What dimensions of the can will require the least amount of material? (i.e., find r and h.)
66cd7582179b4.jpg

Fig. 1. An oil can with radius r and altitude h, both in meters.

(a) 66cd75b299088.jpg；

(b)66cd75d5d85f1.jpg；

(c) 66cd75fd7e03f.jpg.

3. (15 pts) Evaluate indefinite integral
66cd76315f08e.jpg

4. (20 pts) Find the length of the cardioid r = a(1 - cos θ), as shown in Fig 2.
66cd766a0c0da.jpg
Fig. 2. The cardioid r = a(1 - cos θ).
5. (20 pts) Find the maximum and minimum distances from the origin to the curve 5x² + 6xy + 5y² = 8.
6. (15 pts) Find the general solution on the interval (-∞, +∞) of the differential equation
y''-2y' y=ex+e2x.