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研究所、轉學考(插大)-微積分
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99年 - 99 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#113207
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1. Evaluate the indefnite integral
dx.
Answer : __________________
其他申論題
6. (12%) Evaluate
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7. (12%) Use polar coordinates to combine the sum into one double integral . Then evaluate the double integral.
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8. (12%) Show thatconverges and finds its sum .
#483626
9. (12%) Find the local maximun and minimum values and saddle point(s) of the function f(x,y)=x3+y3+3x2-3y2-8
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2. Find the points on the graph of z = 3x2 - 4y2 at which the vector n=(3, 2,2) is normal to the tangent plane. Answer :____________
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3. What is the value of the double integral dxdy? Answer :__________
#483630
4.What is the largest value that the directional derivative of f(x,y, z) = xyz can have at the point (1,1,1)? Answer :___________
#483631
(a) Determine if the series converges or diverges? (5分)
#483632
(b) Determine if the improper integral converges or diverges?(5分)
#483633
2. Find the maximum area of a rectangle inscribed in the ellipse =1.(10分)
#483634
dx.
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dx.