102年 - 102 國立臺灣師範大學_轉學生招生考試試題_地球科學系二年級：微積分#118413

科目：研究所、轉學考(插大)-微積分 | 年份：102年 | 選擇題數：0 | 申論題數：15

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所屬科目：研究所、轉學考(插大)-微積分

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申論題 (15)

1. Let f(x)=2cosx+tan2x.Then f'(x)=________

(a) the increasing intervals:__________

(b) local maximum values: __________

(c) local minimum values:__________

(d) intervals of concavity: __________

(e) inflection points:__________

3.=________

(a) f'(x)=________

(b)=________

5.=________

6. Find the extrema of f(x,y,z)=x²+y²+z² subject to the constraint x+y+z=9.

7. Let C be the curve given by y=4x-x² from (4,0) to (1,3). Then =________

8. Let f(x,y,z)= and S=.Then =________

9. Rewrite the integral

as the integral with the order of integration dzdydx:__________

10. Let C be any counterclockwise and simple closed curve. Find the maximum of the line integral :__________