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  • Need solution for RD Sharma maths class 12 chapter Differentials Errors and Approximations exercise 13.1 question 9 sub question (xviii)

Need solution for RD Sharma maths class 12 chapter Differentials Errors and Approximations exercise 13.1 question 9 sub question (xviii)

Answers (1)

Answer: 5.1

Hint:Here, we use the formula

        \Delta y=f(x+\Delta x)-f(x)

Given:\sqrt{26}

Solution:  Consider the function y=f(x)=\sqrt{x}

Let

        \begin{aligned} &x=25 \\\\ &x+\Delta x=26 \end{aligned}

Then,

        \begin{aligned} &\Delta x=2 \\\\ &\text { For } x=25 \\\\ &y=\sqrt{25}=5 \end{aligned}

Let,

        d x=\Delta x=1

Now

        y=(x)^{\frac{1}{2}}

        \begin{aligned} &\frac{d y}{d x}=\frac{1}{2 \sqrt{x}} \\\\ &\left(\frac{d y}{d x}\right)_{x=25}=\frac{1}{10} \\\\ &\Delta y=d y=\frac{d y}{d x} \times d x=\frac{1}{10} \times 1=0.1 \end{aligned}

        \begin{aligned} &\Delta y=0.1 \\\\ &\sqrt{26}=y+\Delta y=5.1 \end{aligned}


 

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