世新大學九十三年學年度第二部二年級轉學生考試

系所別	考試科目
資訊管理學系	微積分

※不可使用計算機(依世新大學入學考試試場規則，考生僅能使用等功能之簡易計算機型)

※考生請於答案卷內作答

1. (20 points, 5 points each)

Compute the following limits

(1) lim (2) lim (3) lim

(4) lim

2. (20 points, 10 points each)

(1) Prove the Fundamental Theorem of Calculus:

If is continuous on and F(x)=,then F

(2) If F(x)= F’(x).

3. (20 points, 5 points each)

Evaluate the following integrals.

(1) (2) (3)

(4) (5)

4. (10 points, 5 points each)

Compute the derivatives of the following functions.

(1) (2)

5. (15 points)

Sketch the graph of and show all significant features.

6. (10 points)

Find the area of the region bounded by the graphs of