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  • Explain solution RD Sharma class 12 chapter Differentials Errors and Approximations exercise 13.1 question 9 sub question (xv) maths

Explain solution RD Sharma class 12 chapter Differentials Errors and Approximations exercise 13.1 question 9 sub question (xv) maths

Answers (1)

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Answer: 2.9907

Hint: Here we use  \Delta y=f(x+\Delta x)-f(x)

Given: x=(80)^{\frac{1}{4}}

Solution:  x=81

\begin{aligned} &\Delta x=-1 \\\\ &\Rightarrow y=\frac{1}{4}=f(x) \\\\ &\frac{d y}{d x}=\frac{1}{4}=x^{\frac{-3}{9}} \end{aligned}

\begin{aligned} &\Rightarrow \text { at } x=81, \frac{d y}{d x}=\frac{1}{4} x 81^{\frac{-3}{9}} \\\\ &=\frac{1}{4} \times 3^{\frac{-3 \times 4}{4}}=\frac{1}{4.3^{3}}=0.009252925 \end{aligned}

\begin{aligned} &\Delta y=\Delta x \times \frac{d y}{d x} \\\\ &=-1 \times 0.00925925 \\\\ &=-0.00925925 \end{aligned}

\begin{aligned} &\text { Also, } A y=f(x+\Delta x)-f(x) \\\\ &f(x+\Delta x)=\Delta y+f(x) \\\\ &(80)^{\frac{1}{4}}=-0.00925925 \\\\ &=2.990740741 \end{aligned}


 

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