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  • Explain solution RD Sharma class 12 chapter Differentials Errors and Approximations exercise 13.1 question 12 maths

Explain solution RD Sharma class 12 chapter Differentials Errors and Approximations exercise 13.1 question 12 maths

Answers (1)

Answer: 3.0021715

Hint: Here we use this below formula

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

Given:  \log _{10} e=0.4343

Solution: Let: y=f(x)=\log _{10} x

⇒  Here,

\begin{aligned} &x=1000 \\\\ &x+\Delta x=1005 \\\\ &\Delta x=5 \\\\ &d x=\Delta x=5 \end{aligned}

\begin{aligned} &\text { For } x=1000 \\\\ &y=\log _{10} 1000=\log _{10}(10)^{3}=3 \\\\ &\Rightarrow \text { Now } y=\log _{10} x=\frac{\log e x}{\log e 10} \\\\ &\frac{d y}{d x}=\frac{0.4343}{x} \end{aligned}

\begin{aligned} &\left(\frac{d y}{d x}\right)_{x=1000}=\frac{0.4343}{1000}=0.00043 \\\\ &\Delta y=d y=\frac{d y}{d x} \times d x=0.0004343 \times 5=3.0021715 \end{aligned}

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