99年 - 99 國立高雄大學轉學生招生考試試題(轉二年級)_應用物理學系、電機工程學系、資訊工程學系：微積分#116013

科目：研究所、轉學考(插大)-微積分 | 年份：99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)

Please show your calculations for each question.

1. Differentiate y = x + arctan y .

2. Find if y^x=x^y.

3. Evaluate .

4. Find the limit .

5. Evaluate the integral dx .

6. Find the area of the region bounded by x+ y = 0 and x=y²+3y .

7. Find the volume of the solid obtained by rotating the region bounded by y=2x and y=x² about the x-axis.

8. Find the slope of the tangent line to r= e^−θatθ = π .

9. Find the volume of the parallelepiped with adjacent edges PQ, PR, and PS, where P =（3,0,1 ) ,Q =(−1,2,5 ), R =(5,1, −1)and S =(0,4, 2 ) .

10. If v＝x²siny+ ye^xy,where x=s+2t and y = st , find ∂v/∂s when s=0 and t=1.