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TN XII Math
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Differential Calculus Applications - II
The radius of a circular disc is given as $24cm$ with a maximum error in mesurement of $0.02cm$ Use differentials to estimate the maximum error in the calculated area of the dise.
This question has multiple parts. Therefore each part has been answered as a separate question on Clay6.com
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exercise6-1
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asked
Apr 24, 2013
by
poojasapani_1
edited
Aug 12, 2013
by
meena.p
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1 Answer
Toolbox:
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 area of the disc is $A=\pi r^2$ where
x is the radius
$\therefore dA=2 \pi x dx$
When $ x=24cm, dx \approx \Delta x =0.02$
$\therefore dA =2 \pi \times 24 \times 0.02$
$\qquad=0.96 \pi cm^2$
answered
Aug 12, 2013
by
meena.p
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