[考古] 幾題積分請各位幫忙~
1.The temperature T(x,y) at points of the xy-plane is given by T(x,y)
= x^2 - 2y^2 . In what direction should an ant at position (2,-1)
move if it wishes to cool off as quickly as possible?
它題目要求溫度能急速下降，表示溫度變化率最大，所以我初步猜測
應該是▽T
(因為T的方向導數(溫度沿某弧長方向的變化率)
dT/ds = ▽T‧T = │▽T│ ≦cosθ)
但它是怎麼判斷該變化率是溫度急遽升高還是下降????
題目要求快速下降，但我不知道結果出來的變化率會導致上升還是下降?
2.Prove
d g(x)
---- ∫ f(u)du = f(g(x))g'(x) .
dx a
此題如果用Leibniz，算不算正當証法?
3.Compute ∫∫ lnx dA , where D is the finite region in the first quadrant
D
bounded by the line 2x+2y = 5 , and the hyperbola xy = 1.
這一題沒加lnx很簡單，加上去以後我就不知道該怎麼積了@@"
x^2 y^2 z^2
4.Find the volume of the region inside the ellipsoid --- + --- + --- =1
a^2 b^2 c^2
and above the plane z = b-y.
這題我主要卡在積分域不知道該怎求~
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※ 編輯: antirazin 來自: 61.230.161.111 (07/05 11:49)
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