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

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.)

(a) ；

(b)；

(c) .

3. (15 pts) Evaluate indefinite integral

4. (20 pts) Find the length of the cardioid r = a(1 - cos θ), as shown in Fig 2.

Fig. 2. The cardioid r = a(1 - cos θ).