Functions of several variables: Total differential and Taylor approximation
Estimating an error
Suppose that you measure three quantities \(x\), \(y\) and \(z\) and need the composite variable \(w=ax- by+ cz\) with \(a\), \(b\) and \(c\). Suppose your measurements are \(x_m\pm {\vartriangle}x\), \(y_m\pm {\vartriangle}y\) and \(z_m\pm {\vartriangle}z\). What is the estimated error of \(w\)?
Denote the errors as differentials, so \(\dd x\) rather than \({\vartriangle}x\), and so on.
Denote the errors as differentials, so \(\dd x\) rather than \({\vartriangle}x\), and so on.
| \(\dd w={}\) |
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