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108年 - 108 國立臺北大學_轉學生招生考試試題_經濟學系二年級：微積分#118416

科目：研究所、轉學考(插大)-微積分 | 年份：108年 | 選擇題數：0 | 申論題數：15

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所屬科目：研究所、轉學考(插大)-微積分

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申論題 (15)

I. (50 points) Fill in the following blanks. 
1. The range of 65839436240d6.jpg is__(1)__.

2. If y2 = x2+sin xy,then6583977e8c4b8.jpg=__(2)__.

3. The value of 658397c3293b3.jpgis __(3)__.

4. Let 65839802633b1.jpg+1,x≥0, then f-1(x)=__(4)__ .(You need indicate x's range too.)
5. Let f be a differentiable one to one function with f(1)=2, f(2)=1,f(3)=0, f'(1)=-6, f'(2)=-2 and f(3)=-1/2. Then, (f-1)'(0)=__(5)__.
6. The absolute minimum valuc of f(x)=x4/3 -x-x1/3 on the interval of [-1, 6] is__(6)__.

7. The value of 658398b4b982d.jpgis__(7)__.

8. The value of 658398e8c451f.jpgis __(8)__.

9. Does series6583991bb0d82.jpg converge or diverge? __(9)__

10.ls65839953396c2.jpglarger? __ (10)__
II. (50 points) Fill in the following blanks.
1. Use the first three terms of the Taylor series to approximatef(x)=x8+x4+3 at x=1. Then, the result is__(1)__.

2. Suppose that f is a continuous function satisfying 658399c412bff.jpgforall x, and c is a real number such that f(c)=1. Then, expressing f'(c) in terms of c only is__(2)__.

3. For limit65839a090fabb.jpgto exist, the value of constant a=__(3)__.

4. Assume that z and w are differentiable functions of x and y,satisfying the equations xw2+yz2+z3=-1 and zw3 -xz3+ y2w=1. Then, at (x,y, z, w)=(I,-1,-1, 1), 65839a6b7fb1c.jpg=__(4)__.

5. The value of65839a9d7763b.jpgis__(5)__.