102年 - 102 國立中山大學轉學生招生考試試題_機電系二年級：微積分#116022

科目：研究所、轉學考(插大)-微積分 | 年份：102年 | 選擇題數：0 | 申論題數：6

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 (6)

1. (15 points) Let 1 +e^xy = y²+x. Find in terms of n and y.

2. (15 points) Determine whether the series converges or diverges.

3. (15 points) Evaluate

4. (15 points) Let F(x,y,z) = x² - y²z. What is the direction of greatest increases for the function F at the point (1,2,3)?

5. (20 points) Use the method of Lagrange multipliers to find the point on the plane x + 2y + 3z = 6 that is nearest to the origin.

6. (20 points) Evaluate the integral

where C is the the right triangle with vertices (0,0), (0,2), and (1,0).