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  • Please solve RD Sharma class 12 chapter 13 Differentials Errors and Approximations exercise multiple choice question 11 maths textbook solution

Please solve RD Sharma class 12 chapter 13 Differentials Errors and Approximations exercise multiple choice question 11 maths textbook solution

Answers (1)

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Answer: 2.0125

Hint: Here, we use the formula of \Delta y=d y=\frac{d y}{d x} \times d x

Given: 33^{\frac{1}{5}}

Solution:

Consider the function

        y=f(x)=x^{\frac{1}{5}}

Let x=32

        x+\Delta x=33

So,

        \text { } \begin{aligned} &\Delta x=1 \\\\ &y=x^{\frac{1}{5}} \text { for } x=32 \Rightarrow \mathrm{y}=2 \end{aligned}

        \frac{d y}{d x}=\frac{1}{5(x)^{\frac{4}{5}}}

Also

            \begin{aligned} &\left(\frac{d y}{d x}\right)_{x=32}=\frac{1}{80} \\\\ &\Delta y=d y=\frac{d y}{d x} \times d x \\\\ &=\frac{1}{80} \times 1 \\\\ &=0.0125 \end{aligned}

so,

            \begin{aligned} (33)^{\frac{1}{5}} &=y+\Delta y \\\\ &=2+0.0125 \\\\ &=2.0125 \end{aligned}

 

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