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

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

Answers (1)

Answer: 0.191667

Hint: Here we use the formula

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

Given: (0.007)^{\frac{1}{3}}

Solution: consider the function f(x)=3 \sqrt{x}

Let:

\begin{aligned} &x=0.008 \\\\ &x+\Delta x=0.007 \end{aligned}

Then,

\begin{aligned} &\Delta x=-0.001 \\\\ &\text { For } x=0.008, \end{aligned}

\begin{aligned} &y=\sqrt{0.008}=0.2 \\\\ &\text { Let, } d x=\Delta x=0.001 \\\\ &\text { Now } y=3 \sqrt{x} \end{aligned}

\begin{aligned} &\frac{d y}{d x}=\frac{1}{3(x)^{\frac{2}{3}}} \\\\ &\left(\frac{d y}{d x}\right) x=0.008=\frac{1}{0.12} \times 0.001=\frac{1}{120} \end{aligned}

\begin{aligned} &\Rightarrow \Delta y=\frac{1}{120}=0.008333 \\\\ &(0.007)^{\frac{1}{3}}=y+\Delta y=0.191667 \end{aligned}

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