109年 - 109 國立高雄大學_碩士班招生考試_應用數學系：微積分#103317

科目：研究所、轉學考(插大)-微積分 | 年份：109年 | 選擇題數：0 | 申論題數：15

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 (15)

(a) If f(x) ＜ g(x) for all

(b) The graph of every cubic polynomial has precisely one point of inflection.

(c) It is possible to find a power series whose interval of convergence is [0,∞).

(d) The polar equations r = sin 2θ, r = − sin 2θ, and r = sin (−2θ) all have the same graph.

(e) Two different level curves of the graph of z = f(x, y) can intersect.

2. Find the derivative of

3. Determine whether converges or diverges. Identify the test used.

4. Let , x ＞ 2. Verify that f has an inverse function and find .

5. Evaluate

6. Find the unit tangent vector and the principal unit normal vector to the curve .

7. Show that fx(0, 0) and both exist but that f is not differentiable at (0, 0).

(a)

(b)

(c)

(d)