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研究所、轉學考(插大)-微積分
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103年 - 103 國立成功大學轉學生招生考試試題_微積分_(理工系所聯招)#113219
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7. (10 points) Determine and classify the stationary points of the function f(x,y)=xy(3x+6y-2).
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(b) (6 points)
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(a) (6 points) Find the convergence set of
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(b) (8 points)Evaluate
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6. (10 points) DefineProve that：
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8. (10 points) Find the total arc length of the cardioid r = a(1-cosθ),a＞0.
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9. (10 points) Use change of variablesto evaluate the integral , where
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1. Let If the function f is continuous on the entire real line. Then a =_________.
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2. Let Then fxy(0,0) = f(x, y) = and fyx(0,0) =__________.
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3. Let f(x) = .Then the interval of convergence of f(x) is________. and the interval OF convergence of f'(x) is________.
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4. Let R be the region inside the ellipsoid where a,b,c> 0, and abovethe plane z = b-y, then the volume of the region R is =______.
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