105年 - 105 國立臺灣師範大學_轉學生招生考試試題_機電工程學系二年級：微積分#120160

科目：研究所、轉學考(插大)-微積分 | 年份：105年 | 選擇題數：0 | 申論題數：9

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 (9)

1.Find .(10分)

2. Find [sin(In x)dx.(10分)

3. Find . Hint: Use the polar coordinate system. (10 分)

4. Determine the minimum area of a triangle form by the x axis, the y axis, and a line through the point (a,b). Here, a and b are positive constants. (10 分)

5. Find .

6. Find In x dx. This is the area of the region bounded by the graph of y= xInx and the x axis.(15分)

7. Find the directional derivative of the function f(x,y)=(x+y)/(x-y) at point (1,-1) in the direction v=.(10分)

8. Find the area of the region T bounded by the parabolas y=x² and y=4-x². (10分)

9. Find the point within a given triangle for which the sum of the squares of its perpendicular distances to the sides is least. ( 15 分)