大學微積分方向導數問題

2014-05-27 7:42 am

題目是
Estimate how much ____ the value of f(x,y,z)=ysinx+2yz will change if the
point P(x,y,z) move 0.1 units from P0(0,1,0) straight toward P1(2,2,-2)
利用df=∇f‧dr
算出來是-1/15

但我把(0,1,0)與移動0.1單位後的座標(1/15,31/30,-1/15)代入f後相減，算出來的值並不是-1/15，是哪裡出問題嗎？還是我觀念不清楚？

回答 (9)

鞍點墨玉玉器

2014-05-27 4:11 pm

✔ 最佳答案

f(x,y,z)=ysinx+2yz
Δf = (D1f,D2f,D3f)，D1f=partial differential of at x
Δf = (ycosx, sinx+2z, 2y)

The point P(x,y,z) move 0.1 units from P0(0,1,0) straight toward P1(2,2,-2)，
and the moving vector V = (2, 1, -2)
the scale change is 0.1/｜V｜ = 1/30
dr = V/30 = (1/15, 1/30, -1/15)
Δf (0,1,0) = (1, 0, 2)
df=∇f‧dr =(1, 0, 2)‧(1/15, 1/30, -1/15) = -1/15

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[匿名]

2014-06-21 10:05 pm

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[匿名]

2014-06-20 9:12 pm

到下面的網址看看吧

▶▶http://candy5660601.pixnet.net/blog

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EQVWOHTQXJCD

2014-06-05 1:14 pm