Difference between revisions of "TF ErrorAna PropOfErr"
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<math>f(x) = f(a) + f^{\prime}(x)|_{x=a} \frac{x}{1!} + f^{\prime \prime}(x)|_{x=a} \frac{x^2}{2!} + ...</math> | <math>f(x) = f(a) + f^{\prime}(x)|_{x=a} \frac{x}{1!} + f^{\prime \prime}(x)|_{x=a} \frac{x^2}{2!} + ...</math> | ||
;<math>= \sum_{n=0}^{infty} f^{(n)}(x)|_{x=a} \frac{x^n}{n!}</math> | ;<math>= \sum_{n=0}^{infty} f^{(n)}(x)|_{x=a} \frac{x^n}{n!}</math> | ||
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| + | For small values of x we can expand functions about 0 such that | ||
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| + | \sqrt(1+x) = \sqrt(1-0) | (1+x)^{-1/2} | ||
Revision as of 19:58, 9 January 2010
A quantity which is calculated using quantities with known uncertainties will have an uncertainty based upon the uncertainty of the quantities used in the calculation.
To determine the uncertainty in a quantity which is a function of other quantities, you can consider the dependence of these quantities in terms of a tayler expansion
Consider a calculation of a Table's Area
The mean that the Area (A) is a function of the Length (L) and the Width (W) of the table.
The Taylor series expansion of a function f(x) about the point a is given as
For small values of x we can expand functions about 0 such that
\sqrt(1+x) = \sqrt(1-0) | (1+x)^{-1/2}