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研究所、轉學考(插大)-微積分
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99年 - 99 國立暨南國際大學轉學生招生考試試題_資工系二：微積分#124194
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1. (10%)以ε-δ證明 (i.e. find the largest δ that works for the given ε)
= 2.
其他申論題
8. 求線積分之值，其中曲線C的方程式為x2+y2=49。
#527893
(a)
#527894
(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
(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
4. (10%) Estimate f (5.4) given that f (5)=1 and f'(x) = .
#527901
5. (10%) Find the volume of the solid generated by revolving the regionbetween y = , 0 ≤ x ≤ 1 and y= x², 0 ≤ x ≤ 1, around the line x = -2.
#527902
6. (10%) Find the least upper bound and greatest low bound of the sequence.
#527903
= 2.
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= 2.