# 107 年 - 107 台灣綜合大學系統學士班轉學生聯合招生試題：微積分A#96949

【非選題】
1.
1. (10 Points) Evaluate:

【題組】

(a) (5 Points) 【非選題】
2.【題組】

(b)(5 Points) 【非選題】
3.

2. (10 Points) Find the point on the curve y = that is closest to the point .

【非選題】
4.

3. (10 Points) Find the length of the parametric curve
x=3t2,y=2t3, 0 ≤ t ≤ 1

【非選題】
5.

4. (10 Points) Determine whether the improper integral is convergent or divergent.

【非選題】
6.

5. (10 Points) Find the radius of convergence of the power series and evaluate 【非選題】
7.

6.(10 Points) Find the equation of the tangent plane and the normal line to the surface at (1,1,0).

【非選題】
8.

7.(10 Points) Let f : be a function. Assume that all second partial derivatives of f exist and continuous and Deine g : 【非選題】
9.

8. (10 Points) Evaluate the double integral , sin(x+y)dA where D is the regsion bounded by x+y= π, x+y = 0 and x -y =π and x-y=0.

【非選題】
10.

9.(10 Poins) Evaluate the triple integral , where E is the solid region in bounded by the surface z = 1 and z = x2+y2.

【非選題】
11.

10. (10 Points) Evallate the line interal along the curve C : r(t) = (t2+1)i+ (t2 - 1)j, 0 ≤ t ≤ 2. Hint you may find a potential function f of the vector field F(x,y) = find f so that F = ∇f.

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