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  • Please solve RD Sharma class 12 chapter Differentials Errors and Approximations exercise 13.1 question 9 sub question (xxviii) maths textbook solution

Please solve RD Sharma class 12 chapter Differentials Errors and Approximations exercise 13.1 question 9 sub question (xxviii) maths textbook solution

Answers (1)

Answer: 31.920

Hint: Here we use this below formula

        \Delta y=f(x+\Delta x)-f(x)

Given: (1.999)^{5}

Solution: \operatorname{let} x=2 \text { and } \Delta x=-0.001

\text { Let } y=x^{5}

on differentiating both side wrt we get

\begin{aligned} &\frac{d y}{d x}=5 x^{4} \\\\ &\text { Now, } \Delta y=\frac{d y}{d x} \Delta x=5 x^{4} \times \Delta x \\\\ &=5 \times 2^{4} \times[-0.001]=-80 \times 0.001 \end{aligned}

\begin{aligned} &=-0.080 \\\\ &(1.999)^{5}=y+\Delta y=2^{5}+(-0.080) \\\\ &=32-0.080 \\\\ &=31.420 \end{aligned}

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