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研究所、轉學考(插大)-微積分
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98年 - 98 國立暨南國際大學_轉學生入學考試試題_資工系二：微積分#124587
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題組內容
7. (10%)The sequence {aₙ} defined by
(a) (2%) Show that it is increasing.
其他申論題
3. (10%) Find the volume of the solid generated by revolving the regionbounded by y=x² and y=2x about the x-axis.
#529869
4. (10%) Definition: The function ln(x) = , x ＞ 0, is called the natural logarithm function. Prove that In(ab) = ln(a) + In(b) for a, b ＞ 0.
#529870
5. (10%) Find the function f(x), such that f(t)dt = -5.
#529871
6. (10%) Evaluate
#529872
(b) (3%) Find the greatest lower bound.
#529874
(c) (5%) Find the least upper bound.
#529875
8. (10%) Verify that the improper-integral diverges.
#529876
9. (10%) Show that the series converges on [-1, 1).
#529877
10. (10%) Use the chain rule to find the rate of change of f(x,y) = (x3 + y3) with respect to t along the curve r(t) = cos(t) i + sin(t) j.
#529878
(1)=_________
#529879
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