101年 - 101 國立中山大學轉學生招生考試試題_機電系：微積分#118420

科目：研究所、轉學考(插大)-微積分 | 年份：101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)

1. (a) Let f(x) =.Find f'(x).

(b) Find an equation of the tangent line of the ellipse x²+4y²= 4 at .

2. (a) Evaluate

(b) Evaluate sin x dx, where s ＞ 0.

3. (a) Find the Taylor series of f(x) = at x = -1.

(b) Determine the interval of convergence of

4. (a) Find the direction in which f(x, y) = x² - xy - y² decreases fastest at (1,1).

(b) Find the extreme values of f(x, y) = x²+y²-2x-2y-2 over R=[0,2]x[0,3].

5. (a) Is the vector field F(x, y) = y²i +xyj conservative?

(b) Find curl F, where F(x,y,z) = xyi- xyzj + x²k.