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Experimal error calc

  1. Feb 5, 2008 #1
    x = s(sqrt((2(a+b))/zab)

    There is error in s, a and b

    show the required result is

    [tex]\Delta[/tex]x/x = sqrt( (1/(4ab)^2)*[(b[tex]\Delta[/tex]a/a)^2+(a[tex]\Delta[/tex]b/b)^2]+([tex]\Delta[/tex]s/s)^2
     
    Last edited: Feb 5, 2008
  2. jcsd
  3. Feb 5, 2008 #2

    HallsofIvy

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    Staff Emeritus
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    What happened to the "z" in the denominator? I don't see it in the result? Is it a typo?

    Try this: take the logarithm of both sides so
    ln(x)= ln(s)+ (1/2)[ln(2)+ ln(a+b)- ln(a)- ln(b)- ln(z)]

    Now take the differential:
    dx/x= ds/s+ (1/2)[(da+db)/(a+b)- da/a- db/b- dz/z] and replce each "d" with "[itex]\Delta[/itex].
     
  4. Feb 5, 2008 #3
    z has no error associated with it
     
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