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研究所、轉學考(插大)-微積分
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105年 - 105 國立臺南大學_轉學生招生考試試題_理工聯招二年級：微積分#124196
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7. Evaluate the double integral
, where
D≔{(x,y)| 0≤x≤2,1≤y≤2}.
其他申論題
3. Show that .
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4. Evaluate =?
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5. Evaluate =?
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6. Let P(1,1,0) and f(x,y)=x3 y-xy3. Please find an equation of the tangent plane to z=f(x,y) at P.
#527925
8. Evaluate +xdy, where C is a line segment from (-5,-3) to (0,2).
#527927
9. Let E≔{(x,y,z)| x2+y2 ≤ z ≤ 1} with the boundary ∂Eand n be the outward-pointing normal vector. Given a vector fieldF(x,y,z)=(+2x-sinz,x-cosz,sin sin(y2)-z2).Please evaluate
#527928
10. Determine if the series converges. Prove or disprove it.
#527929
(a)
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(b)
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(c)
#527932
, where 
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, where