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Uncertainty as power.

  1. Dec 31, 2012 #1
    1. The problem statement, all variables and given/known data

    Book: Introduction to error analysis, Taylor

    In page 66, quick check 3.8

    If you measure x = 100[itex]\pm[/itex] 6, what should you report for [itex]\sqrt{x}[/itex]with its uncertainty.

    2. Relevant equations

    Rule for uncertainty as power:
    [itex]\frac{∂q}{|q|}[/itex] = |n|[itex]\frac{∂x}{|x|}[/itex]


    where [itex]q = x^{n}[/itex]

    3. Attempt

    So our function is q = [itex]x^{\frac{1}{2}}[/itex]

    then σq = 0,3. (as in solution)


    The problem that is killing me is if i decide to use the general rule for error propagation, the result is different.

    Using that rule:

    |σq| = |[itex]\frac{∂q}{|x|}| Δx = | \frac{1}{2\sqrt{x}} |Δx [/itex]
    That gives:

    |σq| ≈ 0,3


    After all, the problem is correct. It was just bad calculations.

    I do not to know how to delete topics. :/
     
    Last edited: Dec 31, 2012
  2. jcsd
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