課程名稱︰微積分乙
課程性質︰系定必修
課程教師︰黃漢水
開課系所︰管院的系
考試時間︰6/22
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
１.Find the equation of the tagent plane to the surface
xy^2 + 3xz - 2yz + 33 = 0 at the point (-1,2,3) (20%)
２.Let D = {(x,y,z) | x^2 + y^2 + z^2 = 50} and the temperature at
the point (x,y,z) on the D is T(x,y,z) = 6xy + 8yz
Find the highest and the lowest temperatures. (20%)
2 4
３.Find the integral ∫ ∫ x[(y^2+9)]^1/2 dydx (20%)
0 x^2
４.Let D = {(x,y) | (x - 3)^2 + y^2 ≦ 9 , y ≧ 0} be a thin plate.
Suppose the density at the point (x,y) is den(x,y)=(x^2 + y^2)^1/2
Find the mass of D. (20%)
５.Let D ={(x,y,z) | x^2 + y^2 +z^2 ≦ 25 , z ≧ 0}.
Find the integral ∫∫∫(x^2 + y^2 + z^2)^1/3 dxdydz (20%)
D
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