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99年 - 99 國立臺南大學_轉學生招生考試試題_應用數學系二年級：微積分#124193
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題組內容
9. 判斷下列級數是收斂或發散？
(a)
其他申論題
5. A rectangular box without a top is to have a volume of 12 cubic feet. Find the dimensions of the box that will have minimum surface area.
#527890
6. 求極限=?
#527891
7. 求不定積分=?
#527892
8. 求線積分之值，其中曲線C的方程式為x2+y2=49。
#527893
(b)
#527895
10. 已知此平面x+y+z=1與圓柱x2+y2=1相交為一個橢圓，求此橢圓上距離圓點最近與最遠的點？
#527896
1. (10%)以ε-δ證明 (i.e. find the largest δ that works for the given ε)= 2.
#527897
(a) (10%) Please describe the mean-value theorem and prove it.
#527898
(b) (10%) Set f(x)= x-1, a = -1, b=1. Verify that there is no number c for which f'(c)=[f(b)-f(a)]/(b-a). Explain how this does not violate the mean-value theorem.
#527899
3. (10%) Find A and B given that the derivative off(x) =is continuous for all x.
#527900
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