98年 - 98 國立高雄大學轉學生招生考試試題(轉二年級) _資訊工程學系、應用物理學系、電機工程學系：微積分#116018

科目：研究所、轉學考(插大)-微積分 | 年份：98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. Find an equation of the tangent to y=(2+x)e^-x at (0, 2). [5 marks]

2. The volume of a cube is increasing at a rate of 10cm³ /min. How fast is the surface area increasing when the length of an edge is 30cm? [5 marks]

3. Evaluate the integral [5 marks]

4. Evaluate the integral sec2θtan2θdθ . [5 marks]

5. Evaluate the integral [15 marks]

6. Evaluate the integral [15 marks]

7. Find the volume of the solid obtained by rotating the region bounded by x = 0 and x=9-y² about x = −1. [15 marks]

8. Find an equation of the curve that passes through the point (1,1) and whose slope at (x,y) is y²/x³ . [10 marks]

9. Find the radius of convergence and interval of convergence for the series . [10 marks]

10. Find equations of the tangent plane and the normal line to the surface z=e^x cos y at (0,0,1). [15 marks]