4.求 ∫sin⁴xdx=? (10%)

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.

1.試證明函數f(x)=在點x0=0處,其極限不存在。 (10%)

2. 求=? (10%)

3. 若y = ,求導數y'=? (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%)

Part 4: Short essay writing 20% (本大題於答案卷作答)Write an essay of approximately 300 words in English. Give your essay a title, and include the following: a) how the different aspects of your life, e.g. life style, study, interpersonal relationship, etc. have changed because of COVID-19,and b) personal reflection from this experience.The maximum score for your essay is 20%. You receive 10 points for content, and another 10 for form such as vocabulary, grammar, sentence variety, and writing skills.Part 4: Short essay