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The radius of a circular disc is given as $24cm$ with a maximum error in mesurement of $0.02cm $ compute the relative error?

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  • Let $y=f(x)$ be a differentiable function then the quantities $dx$ and $dy$ are called differentials.The differential $dx$ is an independent variable.
  • The differential $dy$ is then defined by $dy=f'(x)dx(dx \approx \Delta x)$
  • Also $f(x+\Delta x)-f(x)=\Delta y =dy $ from which $f(x+\Delta x) $can be evaluated
  • $\large\frac{\Delta y}{y}=\frac{Actaual\;change\;in \;y}{Actual\;value\;of \;y}$$=relative \;error$
  • $\large\frac{\Delta y}{y} $$ \times 100 =percentage\; error$
The relative error in area is $\large\frac{\Delta A}{A}=\frac{0.96 \pi}{\pi \times 24}$
$\qquad=\large\frac{0.04}{24}$
$\qquad=\large\frac{0.01}{6}$
$\qquad=0.001667$
answered Aug 12, 2013 by meena.p
 

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