課程名稱︰微積分乙下
課程性質︰
課程教師︰王藹農
開課學院：
開課系所︰
考試日期（年月日）︰96/06/17
考試時限（分鐘）：110分鐘
是否需發放獎勵金：是
（如未明確表示，則不予發放）
試題 :
4xy
1. f(x,y) = ─────── Find max, min, and saddle points (5/50)
(x^2+1)(y^2+1)
2. (x,y) = (-2,0) , (0,1) , (2,3) Find the least squares regression line
y = mx+b = ? (5/50)
3. Find the highest point of the circle x^2+y^2+z^2 = 6 , 2x+y-z = 2 (5/50)
4. u = u(x,y) x = rcosθ , y = rsinθ , second partial derivative
(用 σ 代表偏微符號)
σ^2 u σ^2 u σ^2 u σ^2 u σu σu
─── = ? ─── + ? ─── + ? ─── + ? ─── + ? ─── (5/50)
σy^2 σr^2 σrσθ σθ^2 σr σθ
3 x (9-x^2) ? ? ?
5. ∫∫∫ f(x,y,z) dzdydx = ∫∫∫ f(x,y,z) dxdzdy (5/50)
0 0 0 ? ? ?
6. ∫∫ (x+y)^2‧sin^2(x-y) d△ = ? R is the region of a square with
R (5/50)
vetices (0,1) (1,2) (2,1) (1,0)
_______
7. Find the surface area. Z=√(1-y^2) , 0≦x≦y≦1 (5/50)
→ x → y → → → →
8. F = ─── i + ─── + j + k , r = (x,y,z) , dr = (dx,dy,dz)
x^2+y^2 x^2+y^2
q → →
p = (1,2,3) , q = (4,5,6) , ∫ F‧dr = ? (5/50)
p
ydx - xdy
9. ∫ ────── = ? C is the segment from (1,1) to (2√3,2) (5/50)
C x^2 + y^2
→ → → →
10. F = 2yi + 3zj + xk C is the triangle (0,0,0) (0,2,0) (1,1,1)
→ →
∫ F‧dr = ? (5/50)
C
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※ 編輯: WiNtErPoWeR 來自: 140.112.240.7 (06/17 20:53)