109年 - 109 國立臺北大學_轉學生招生考試試題_通訊工程學系二年級：微積分#117924

科目：研究所、轉學考(插大)-微積分 | 年份：109年 | 選擇題數：0 | 申論題數：7

試卷資訊

所屬科目：研究所、轉學考(插大)-微積分

選擇題 (0)

申論題 (7)

1. (15%) Use the Lagrange multipliers to find the extreme values of f(x, y) = x2 + 2y2 on the circle x2+y2=1
2.(10%) Find y' if xy = yx.
3.(25%) Sketch the curve y = e-1/(x+1)
(You need to describe (a) domain, (b) intercepts, (c) asymptotes (horizontal and vertical if any), (d) intervals of increase and decrease, (e) local maximum and minimum values, (f) interval of concavity, (g) point of inflection, and (h) sketch the curve)

(a)6572d2f50224a.jpg

(b) 6572d310351f5.jpg

5. (20%) Find the volume of the solid generated by revolving the region bounded by 6572d32c9ab13.jpg and the lines y = 2 and x = 0 about(a) the line y = 2,(b) the line x = 4.

6. (20%) Find the first four nonzero terms in the Maclaurin series for(a)6572d359de139.jpg，and (b) sin-1x = 6572d38c23e16.jpgdt.