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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