課程名稱︰微積分乙下
課程性質︰必修
課程教師︰王藹農
開課學院：社科院
開課系所︰
考試日期（年月日）︰99/06/22
考試時限（分鐘）：110 (0810~1000)
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
(範圍：Larson & Edward, Calculus, 9e, 13.9 Lagrange Multiplier - end)
(Ch.14 Multiple Integration Ch.15 Vector Analysis)
1. Find the highest point on the curve of intersection of the surfaces
2 2 2
x + y + z = 4 , x+2y+3z=6 (5/50)
4 2 3
2.∫∫ ---------- dydx=? (5/50)
0 √x 2+y^3
2 4 √(y^2-4x^2) ? ? ?
3.∫∫ ∫ f(x,y,z) dzdydx = ∫∫∫ f(x,y,z)dxdydz (5/50)
0 2x 0 ? ? ?
1 1-u dv
4.∫ (∫ ------------- ) du =? (5/50)
1/2 0 1-u^2+v^2
-x -2x
∞ e - e
5.∫ ------------- dx =? (5/50)
0 x
2 2
2 2 x y
6. Io = inertia = ∫∫ (x + y ) dxdy =? where region R={ --- + --- ≦ 1}
R 2 2
a b
(5/50)
7.∮(2x-3y+1)dx -(3x+y-5)dy =? where loop c =
c
triangle from (0,0) to (2,3) to (4,1) and back to (0,0) (5/50)
-y dx + x dy 2 2
8. ∮ ----------------= ? where loop c = {x + (y-1) =4} (5/50)
2 2 oriented counterclockwise.
x + y
→ → → → →
9. r = r (u,v) = ucosv i + usinv j + 2v k , 0≦u≦3, 0≦v≦2π,
surface area = ? (5/50)
dz
10.∫ y dx + x dy + ---- = ? where c =curve from (0,0,1) to (4,4,4)
c z but not necessarily be the straight
line segment.
(5/50)
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