Find the relative error in Z,if Z = frac{A^{4 | vedclass

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Question

(A) Given the expression $Z = \frac{A^{4} B^{1/3}}{C D^{3/2}}$.According to the rules of propagation of errors,for a quantity $Z = \frac{A^p B^q}{C^r

Vedclass · Accepted Answer

$\frac{\Delta Z}{Z} = 4\frac{\Delta A}{A} + \frac{1}{3}\frac{\Delta B}{B} + \frac{\Delta C}{C} + \frac{3}{2}\frac{\Delta D}{D}$

Vedclass · Answer

(A) Given the expression $Z = \frac{A^{4} B^{1/3}}{C D^{3/2}}$.According to the rules of propagation of errors,for a quantity $Z = \frac{A^p B^q}{C^r D^s}$,the relative error is given by $\frac{\Delta Z}{Z} = p\frac{\Delta A}{A} + q\frac{\Delta B}{B} + r\frac{\Delta C}{C} + s\frac{\Delta D}{D}$.Applying this to the given equation,the powers are $p=4$,$q=1/3$,$r=1$,and $s=3/2$.Therefore,the relative error in $Z$ is $\frac{\Delta Z}{Z} = 4\frac{\Delta A}{A} + \frac{1}{3}\frac{\Delta B}{B} + \frac{\Delta C}{C} + \frac{3}{2}\frac{\Delta D}{D}$.

Find the relative error in $Z$,if $Z = \frac{A^{4} B^{1/3}}{C D^{3/2}}$.

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