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

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Answer: 7.904

Hint: Here we use this below formula

        \Delta y=f(x+\Delta x)-f(x)

Given: (3.968)^{\frac{3}{2}}

Solution: \text { let } y=f(x)=x^{\frac{3}{2}}, x=4

\begin{aligned} &x+\Delta x=3.968 \\\\ &\Delta x=-0.032 \\\\ &\Delta y=\left[\frac{d y}{d x}\right]_{x=4} \times \Delta x \end{aligned}

\begin{aligned} &\Delta y=\left[\frac{3}{2} x^{\frac{1}{2}}\right]_{x=4} \times \Delta x \\\\ &\Delta y=\frac{3}{2} \times 2(-0.032)(0.096) \\\\ &(3.968)^{\frac{3}{2}}=f(x+\Delta x) \end{aligned}

\begin{aligned} &=f(x)+\Delta y \\\\ &=8-0.096 \\\\ &=7.904 \end{aligned}


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