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

Answers (1)

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Answer: 0.2495

Hint: Here, we use the formula

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

Given: $\frac{1}{(2.002)^{2}}$

Solution:

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,

$-0.005=\frac{1}{(2.002)^{2}}-\frac{1}{4}$

We get

$\frac{1}{(2.002)^{2}}=0.2495$

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