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  • Provide solution for RD Sharma maths class 12 chapter 13 Differentials Errors and Approximations exercise multiple choice question 6

Provide solution for RD Sharma maths class 12 chapter 13 Differentials Errors and Approximations exercise  multiple choice question 6

Answers (1)

Answer:    (C)  1.3893

Hint: We all know that

            \Delta y=d y=\frac{d y}{d x} \times d x

Given:

                \log _{e} 4=1.3868

Solution:

Consider the function,

            y=f(x)=\log_{e} x

Let x=4

So,

            \begin{aligned} &x+\Delta x=4.01 \\\\ &\Delta x=0.01 \text { for } x=4 \\\\ &y=\log _{e} 4=1.3868 \\\\ &y=\log _{e} x \end{aligned}

Let’s differentiate,

            \begin{aligned} &\frac{d y}{d x}=\frac{1}{x} \\\\ &\left(\frac{d y}{d x}\right)_{x=4}=\frac{1}{4} \end{aligned}

\begin{aligned} \Delta y &=d y=\frac{d y}{d x} \times d x \\\\ &=\frac{1}{4} \times 0.01 \\\\ &=0.0025 \end{aligned}

\begin{aligned} \log _{e} 4.01 &=y+\Delta y \\\\ &=1.3868+0.0025 \\\\ &=1.3893 \end{aligned}

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