3. Use the second Taylor polynomial of f(x) = ln x at x = 1 to approximate ln 1.1 and find a bound for the error in the approximation. (10分)

4. John Mills - the proprietor of Mills Engine Company, a manufacturer of model air-plane engines - finds that it takes x units of labor and y units of capital to producef(x,y) = 100x3/4y1/4units of the product. If a unit of labor costs $100, a unit of capital costs $200, and $200,000 is budgeted for production. Determine how many units should be expended on labor and how many units should be expended on capital in order to maximize production. (10分)

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.

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%)

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%)

115年 - 115 中央警察大學_碩士班入學考試試題_海洋科技組：微積分#139855

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114年 - 114 臺灣綜合大學系統_學士班轉學生考試試題:微積分A#137897

114年 - 114 臺灣綜合大學系統_學士班轉學生考試試題：微積分B#137819

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114年 - 114 台灣聯合大學系統_學士班轉學生考試試題:微積分#137761

114年 - 114 國立臺灣大學_轉學生招生考試_物理學系/土木工程學系/生物環境系統工程學系/生物機電工程學系:微積分(B)#137745

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112年 - 112 國立臺灣大學_碩士班招生考試題：微積分(D)#130254