推 lynnabc236 :也太快被PO上來了吧= = 不是今天稍早才考完= = 04/22 16:51
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、管院
開課系所︰數學系
考試日期（年月日）︰2010/04/22
考試時限（分鐘）：1020-1210 (110min)
是否需發放獎勵金：是
（如未明確表示，則不予發放）
(Larson Edward: Calculus, Ch.10 ~ Ch.13.9)
試題 :
1. r=2-3sinθ Find the area of the inner loop. (4/40)
3
2. Find the area bounded by r= --------- (4/40)
2-cosθ
3. x=θ-sinθ, y=1-cosθ 0≦θ≦2π arclength=? (4/40)
→
4. r(t)=(t, 6/t) t=3 unit normal vector
→
N =(?,?) (4/40)
5. 5/√3 5m
______⊥_____________ Determine the tention in
\ ／ each of the two cables.
\ ／
\ ／ (4/40)
\ ／
\／
|
|
10kg
6. point p=(4,-1,5) line L: x=3, y=1+3t, z=1+t
Find the distance between p & L. (4/40)
→
7. r(t) =(4cost, 3sint, t ) ,t=π, p=(-4,0,π)
curvature K=? (4/40)
x δz δz
8. z=e sin(y+z) -------=? --------=? (4/40)
δx δy
1 4 4
9. f(x,y)=2xy- ---(x +y )+1 Find maximum, minimum and saddle points. (4/40)
2
10. Find the least square regression line for the points
(-3,0) (-1,1) (1,1) (3,2) (4/40)
我以後一定好好唸微積分囧
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