[微積] Precentage Error
A rectangular solid is measured to have length x, width y,
and height z, but each measurement may be in error by 1%
. Fine the estimated precentage error in calculus the
volume is ____?
嗯, 只是來確認一下答案和自己想法有無缺漏...
V(x,y,z) = xyz
dV= (∂V/∂x)dx + (∂V/∂y)dy + (∂V/∂z)dz
= (yz)(0.01x) + (xz)(0.01y) + (xy)(0.01z)
Then the estimated precentage error is
dV/V = [ (yz)(0.01x) + (xz)(0.01y) + (xy)(0.01z) ] / (xyz)
= 0.03 = 3%
手上的解答是寫 [ (1/x) + (1/y) + (1/z) ] / 100
解答的寫法似乎是考慮量測邊長時誤差固定, 而非成一比例,
比如 x ± 1, y ± 1, z ± 1這般...
是我觀念有問題還是解答錯誤?
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http://wiki.answers.com/Q/What_is_the_percent_error_formula
http://www.mathsisfun.com/numbers/percentage-error.html
http://www.physics.ncsu.edu/pylabs/Percent_Error_Difference_211_212.pdf
僅列出幾個, 查到的 Percentage Error 大多都是利用
|Approximate Value - Exact Value|
----------------------------------- × 100%
|Exact Value|
去計算
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wohtp大這邊指的平方在相加應該是指測量學和統計學中,
Σε^2
標準誤差 σ = sqrt( -------- ) ？
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※ 編輯: BaBi 來自: 114.46.112.190 (06/05 01:36)
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