所屬科目：研究所、轉學考(插大)-微積分
2. Let . Find f ' (0) ? _____________
3. Let . What is the maximum value of f (x) ?_____________
4. If , then=?_____________
5. Find the area of the region bounded by the graphs of and g(x) = -x on the interval [0, 1]. _____________
6. =? _____________
7. =? _____________
1. Show that cos x=. (10%)
2. The region bounded by the curve , the x-axis, and the line x = 4 is revolved about the x-axis to generate a solid. Find the volume of the solid by two different methods (Disk method and Shell method). (8%)
(a)
(b)
(c)
(d)
(e)
4. Let . Find f(7)(0). (10%)
5. Let g (x) be the inverse function of f(x ) =x ln x for x ≥ 1 . Find . (10%)
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. Find f ' (0) ? _____________
. What is the maximum value of f (x) ?_____________
, then
=?_____________
and g(x) = -x on the interval [0, 1]. _____________
=? _____________
=? _____________
. (10%)
, the x-axis, and the line x = 4 is revolved about the x-axis to generate a solid. Find the volume of the solid by two different methods (Disk method and Shell method). (8%)
. Find f(7)(0). (10%)
. (10%)