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研究所、轉學考(插大)-微積分
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97年 - 97 台灣聯合大學系統(清、交、陽、中四校聯招)學士班轉學生聯合招生試題：微積分#113210
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題組內容
1. Let f(x) =
(b) Is the derivative function f'(x) continuous at x= 0? Explain. (6 分)
其他申論題
6. The derivative of f(x, y) at P0(1, 2) in the direction of i + j is and in the direction -2j is -3. What is the derivative of f in the direction of -i -2j?Answer :__________
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7.the area of cap cut from the sphere x2 + y2 + z2 == 2 by the cone z =.Answer :__________
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8. Evaluate the line integral f where C consists of line segments joining successively the points (1,0), (I, 1), (-1, 1) and (-1,0). Answer : __________
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(a) Show that f'(0)=0.(6分)
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(a) Find the limit: (6分)
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(b) Let a and b be constants with0 ＜ a ＜ b. Does the sequence {(an +bn)1/n} converges? If it does converge, what is the limit? (6 分)
#483669
(a) A number a is called a fixed point of a function f if f(a) = a. Prove that if f'(x)≠1 for all real numbers x, then f has at most one fied point. (6 分)
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(b) Show that if converges，thenconverges.(6分)
#483671
1 Lemniscate (x2 + y2)2 = x2 -y2 At the point (x,y)= dy/dx=?
#483672
2. If x3+y3= 3xy, then x + y≤max = ?
#483673
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