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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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10. Determine if the series
converges. Prove or disprove it.
其他申論題
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
7. Evaluate the double integral , where D≔{(x,y)| 0≤x≤2,1≤y≤2}.
#527926
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
(a)
#527930
(b)
#527931
(c)
#527932
(d)If f(x)+x2[f(x)]3=10 and f(1)=2,f'(1) =?
#527933
(e)
#527934
(f)
#527935
converges. Prove or disprove it.
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converges. Prove or disprove it.