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111 年 - 111 台灣綜合大學系統學士班轉學生聯合招生試題:微積分A(理工組二年級)#110842 

選擇:0題,非選:11題 我要補題 回報試卷錯誤
【非選題】
1.

1. (10 points) For what values of a and b, a,b≠0, is the following equation true?
  6327e091ab2f9.jpg



【非選題】
2.
2.

【題組】

(a) (5 points) Let f(x) = sec2 x on6327e0bb22bb9.jpg be the inverse function of f. Find (6327e0ce0e24c.jpg)'(4) =



【非選題】
3.【題組】

(b) (5 points) Let f = f(x,y) be a differentiable function of r and y, and let x= rs,y =rts and h(r,s) = f(x,y) = f(rs,r+ s). Assume 6327e11569bab.jpg(1,2) = 2, 6327e12bc0ef2.jpg(1, 1) =________



【非選題】
4.

3. (10 points) If 6327e15883032.jpgdt, on what interval(s) is f increasing?



【非選題】
5.

4. (10 points) Let a > 0 be a constant. Evaluate
6327e1748eeb9.jpg



【非選題】
6.

5. (10 points) Find the area of the region that lies inside the curve r = 4sinθ and outside the curve r = 2.



【非選題】
7.

6. (10 points) For what real values of p does the series 6327e1ac4ccb5.jpg converges?



【非選題】
8.

7. (10 points) Let f(x) be the function defined by the power series
6327e1ccae912.jpg
Try to express f(s) as an elementary function.



【非選題】
9.8. (10 points) Find the global maximum and global minimum of f(x, y, z) = x2+y2+z2 on the surface x2 + 2y2 + 3z2 = 1 by using the method of Lagrange multipliers.

【非選題】
10.

9. (10 points) Evaluate6327e24cf3df9.jpg dA, where R is the region in the first quadrant bounded by lines y = x, y = 3x, and the hyperbolas xy = 1, xy = 3.



【非選題】
11.

10. (10 points) Evaluate the line integral 6327e290ede13.jpgdy, where C is the arc of the the circle x2 + y2 = 4 traversed counter-clockwise from (2,0) to (-2,0).



懸賞詳解

國一生物下第二次

(四) 小藍在山路邊發現一地層,其內所含化石如附圖,已知地層未翻轉,試回答下列問題:【題組】35. 丁地層的植物化石距今約 1 億年,則下...

50 x

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111 年 - 111 台灣綜合大學系統學士班轉學生聯合招生試題:微積分A(理工組二年級)#110842-阿摩線上測驗

111 年 -111 台灣綜合大學系統學士班轉學生聯合招生試題:微積分A(理工組二年級)#110842