105年 - 105 國立暨南大學轉學生招生考試試題_資工系、應化系、土木系、電機系︰微積分#123448

科目：研究所、轉學考(插大)-微積分 | 年份：105年 | 選擇題數：0 | 申論題數：18

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所屬科目：研究所、轉學考(插大)-微積分

選擇題 (0)

申論題 (18)

(b) If p is a polynomial, then lim_x→bp(x) = p(b).

(c) If f'(r) exists, then lim_x→r f(x) = f(r).

(e) If f and g are increasing on an interval I, then fg is increasing on I.

(a) lim_t→0- g(t)

(b) lim_t→0+ g(t)

(c) lim_t→0 g(t)

(e) lim_t→4g(t)

3. (10%) Show that lim_x→0 x² sin

5. (15%) Sketch the graph of

7. (10%) The region R enclosed by the curves y = x and y = x² is rotated about the x-axis. Find the volume of the resulting solid.

8. (15%) A group of engineers is building a parabolic satellite dish whose shape will be formed by rotating the curve y = ax² about the y-axis. If the dish is to have a 10-ft diameter and a maximum depth of 2 ft, find the value of a and the surface area of the dish.