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  • Explain solution RD Sharma class 12 chapter 13 Differentials Errors and Approximations exercise multiple choice question 10 maths

Explain solution RD Sharma class 12 chapter 13 Differentials Errors and Approximations exercise multiple choice question 10 maths

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Answer: n:1

Hint:  Here we use the concept of relative error

            \frac{d y}{y}=\left(\frac{d y}{d x}\right) \Delta x

Given: y=x^{n}

Solution:

        y=x^{n}

Let’s differentiate

        \frac{d y}{d x}=n x^{n-1}

Approximate error in y is

        \begin{aligned} d y &=\left(\frac{d y}{d x}\right) \Delta x \\\\ &=n x^{n-1} \times \Delta x \end{aligned}

Relative error in y is  \frac{d y}{y}=\frac{n}{x} \Delta x

 

Approximate error  x is dx

            \begin{aligned} &=\left(\frac{d x}{d y}\right) \Delta y \\\\ &=\frac{1}{n x^{n-1}} \Delta y \end{aligned}

Relative error in  x  is \frac{d x}{x}=\frac{1}{n x^{n}} \Delta y

Required solution,

            \frac{\frac{n}{x} \times \Delta x}{\frac{1}{n x^{n}} \times \Delta y}=n^{2} x^{n-1} \frac{\Delta x}{\Delta y}

            \begin{aligned} &=\frac{x}{y} \times \frac{n \times x^{n-1} \times \Delta x}{\Delta x} \\\\ &=\frac{n \times x^{n}}{x^{n}} \\\\ &=\frac{n}{1} \end{aligned}

So, ratio is n:1

 

 

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