104年 - 104 國立成功大學轉學生招生考試試題_微積分_(理工系所聯招)#113204

科目：研究所、轉學考(插大)-微積分 | 年份：104年 | 選擇題數：0 | 申論題數：14

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 (14)

(a) (5 points)

(b) (5 points)

(a) (5 points) Find value of A such that f is continuous at x = 0

(b) (5 points) Is f (x) differentiable at x=0? Explain.

(a) (6 points)

(b) (6 points)

4. (10 points)Find

5. (10 points)Find the area of the polar region R common to the two regions bounded by the curve r =-6cosθ and r =2-2cosθ

6. (10 points)Find the volume of the solid that lies under the cone, about the xy-plane, and inside the cylinder x ²+y ²=2x.

7. (10 points)If f (x) = In, find f ⁽ⁿ⁾(0).

8. (10 points)For what value(s) of a does converge?

9. (10 points)Determine and classify the stationary points of the function f(x,y) = x²+y³+6xy-7x-6y.

(a) (4 points) rectangular coordinates with order of integration dzdxdy,

(b) (4 points) spherical coordinates with order of integration dpdφdθ.