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Explain solution RD Sharma class 12 chapter Differentials Errors and Approximations exercise 13.1 question 9 sub question (vii) maths

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Answer: 0.2495

Hint:  Here, we use the formula

            \Delta y=f(x+\Delta x)-f(x)

Given:  \frac{1}{(2.002)^{2}}


consider     y=\frac{1}{x^{2}}

Here     x=2 \text { and } \Delta x=0.002

On differentiating wrt x,

    \frac{d y}{d x}=\frac{-2}{x^{3}}

So we get,

    \Delta y=\frac{d y}{d x} \cdot \Delta x

On substituting the value we get,

    \Delta \mathrm{y}=\frac{-2}{8}(0.002)

On further calculating we get,

    \Delta \mathrm{y}=\frac{-0.5}{1000}=-0.0005

On substitution we get,


We get


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