1.試證明函數f(x)=在點x₀=0處,其極限不存在。 (10%)

III. Composition: 20%"Connection is a basic human need, but being constantly connected to our technology can make us feel more imprisoned than nourished." How does your smartphone affect your social life and productivity? In what ways does it provide you pleasures and emotional outlets? In what ways does it keep you in your own shell? Write a short essay of 100-120 words to reflect on how your smartphone (or tablet, laptop, other personal electronic device you use most frequently) shapes your life now.

III. Composition: 20%How good are you at time management? Do you easily get distracted, feel lazy, and tend to procrastinate? Or,are you a disciplined person who does what you need to when you need to do it? Write a short essay of100-120 words to explain the strategies you use to keep yourself focused on achieving your goals.

2. 求=? (10%)

3. 若y = ,求導數y'=? (10%)

4.求 ∫sin4xdx=? (10%)

5.求x² sin xdx=? (10%)

6.求瑕積分 In xdx=? (10%)

7. 求sin的近似值,使其誤差小於10-5。 (10%)

8.求三重積分dxdydz =? (10%)

9.在一個半徑為「的球內,內接一圓柱體,求出此圓柱體之半徑為多少時,其體積為最大值。 (20%)