100年 - 100 國立成功大學轉學生招生考試_全校:微積分#113205

科目：研究所、轉學考(插大)-微積分 | 年份：100年 | 選擇題數：0 | 申論題數：10

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 (10)

a) , where [x] is the Gauss function,

b) lim.

2. Find the local extrema of f(x) =x² Inx for x ＞0, discuss concavity and find the point of inflection. (12%)

a)

b)

4. Find the area of the surface generated by revolving the curve 6xy= x⁴+ 3 from x= 1 tox= 3 about the x-axis. (12%)

5. Use , prove , and find the sum . (12%)

6. Find the average value of f(x,y) = xy over the quarter circle x² +y²≤1 in the first quadrant. (12%)

7. Evaluate F(x,y) = dt for x＞ 0, y＞ 0. (12%)

8. Find the points on the curve 17x² + 12xy+ 8y² = 100 that are closest to and farthest away from the origin. (12%)