# 108 年 - 108 台灣綜合大學系統學士班轉學生聯合招生試題：微積分A#96946

【非選題】
1.
1. (10 points) Find the following limits.

【題組】

(a) 【非選題】
2.【題組】

(b) 【非選題】
3.

2.(10 points) Evaluate  【非選題】
4.

3. (10 points) Given with a ＞ 0, find a so that F is maximum at x = -2a.

【非選題】
5.

4.(10 points) Find the largest possible area of a triangle with vertices (0, 2), (1,0) and the third vertex on the ellipse 【非選題】
6.

5. (10 points) Evaluate 【非選題】
7.

6. (10 points) Evaluate 【非選題】
8.

7.(10 points) Derive the complete Taylor series expansion for about x = 0. (In the form with a general formula for )

【非選題】
9.

8. (10 points) Given function T(x,y) = 1+ x2-y2 , find the curve γ(t) = (x(t), y(t)) so that γ(0) = (1,4) and γ'(t) = -∇T(γ(t)).

【非選題】
10.

9. (10 points) Find (a,b) with so that
ㆍThe point P = (1,a,b) is on the surface E defined by ㆍThe tangent plane to E at P contains lines 【非選題】
11.

10. (10 points) Evaluate ,where and L is the path from A to B, to C to A and to D as shown below: Note: The path from B to C is circular.