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  • Need solution for RD Sharma maths class 12 chapter 13 Differentials Errors and Approximations exercise very short answer question 3

Need solution for RD Sharma maths class 12 chapter 13 Differentials Errors and Approximations exercise very short answer question 3

Answers (1)

Answer:

             2 \alpha \text { ( } 2 \text { alpha) }

Hint:

Here, we use the concept of approximation.

Given:

Relative error in measuring the radius of circular plan is  \alpha.

Solution:

Let x be the radius and y be the area of the circular plan.

We have,

\begin{aligned} &\frac{\Delta x}{x}=\alpha \quad \text { and } y=x^{2} \\\\ &\frac{d y}{d x}=2 x \quad \quad \frac{\Delta y}{y}=\frac{2 x}{y} \Delta x=\frac{2 x}{x^{2}} \Delta x \end{aligned}                            

\frac{\Delta y}{y}=2 \alpha                            \left[\because \frac{d\left(x^{n}\right)}{d x}=n x^{n-1}\right]

Hence the relative error in the area of the circular plan is 2\alpha

 

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