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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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5. (10%) Find the function f(x), such that
f(t)dt =
-5.
其他申論題
1. (10%) Find an equation for the tangent line to the curve x³+y³=1+3xy² at (2,-1).
#529867
2. (10%) Use a differential to estimate cos 46°. (=1.41421,π=3.14159)
#529868
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
6. (10%) Evaluate
#529872
(a) (2%) Show that it is increasing.
#529873
(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