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

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申論題 (18)

(a) =
(b) If p is a polynomial, then limx→b p(x) = p(b).
(c) If f'(r) exists, then limx→r f(x) = f(r).
(d)
(e) If f and g are increasing on an interval I, then fg is increasing on I.
(a) limt→0- g(t)
(b) limt→0+ g(t)
(c) limt→0 g(t)
(d) g(2)
(e) limt→4 g(t)
3. (10%) Show that limx→0 x2 sin = 0.
(a)
(b)
5. (15%) Sketch the graph of
(a) x(2 + x5) dx
(b) dx
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.