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107年 - 107 國立臺北大學日間學士班暨進修學士班轉學生招生考試試題_經濟學系日間學士班暨進修學士班二年級：微積分#116832

科目：研究所、轉學考(插大)-微積分 | 年份：107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

選擇題 (0)

申論題 (15)

I. (50 points) Fill in the following blanks. 
1. The value of6528a5ce63672.jpgis__(1)__.
2. The tangent line to the curve x2 +xy-y2=1 at point(2,3) is__(2)__.

3. If 6528a61770ecf.jpg=__(3)__.

4.Let6528a6884e8d4.jpg=__(4)__.

5. Let 6528a66c72451.jpg, then f is decreasing on the interval of__(5)__.

6. The absolute maximum value of6528a6bc0ea14.jpg on the interval of [0,∞) is __(6)__.

7. The value of 6528a6ff79e66.jpg is__(7)__.

8. The value of6528a726262e9.jpg=__(8)__.

9. Does series 6528a748bd665.jpgconverge or diverge?__(9)__.

10. Is 6528a774e006a.jpgsmaller?__(10)__
II. (50 points) Fill in the following blanks.
1.Use the first three terms of the Taylor series to approximate f (x) = cos(5x) at x = 0. Then, the result is__(1)__.

2. If y is a differentiable function of x satisfying equation6528a7b665ffe.jpg=__(2)__.

 3. The value of 6528a7e3eb4f2.jpgis__(3)__.
4. Let u=x+y+z,v=xy+yz+zx,w=xyz, and suppose that f(u,v,w) is a differentiable function satisfying f(u,v,w)=x4+y4+z4 forall (x,y,z). Then, fu(2,-1,-2)=__(4)__.

5. The value of 6528a8664a613.jpgdxdy is__(5)__.