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

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

Answers (1)

Answer:  2.0125

Hint: Here we use this below formula

        \Delta y=f(x+\Delta x)-f(x)

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

Solution: (33)^{\frac{1}{5}}=(32+1)^{\frac{1}{5}}

let  y=f(x)=x^{\frac{1}{5}}

        \begin{aligned} &\Rightarrow y+\Delta y=(x+\Delta x)^{\frac{1}{5}} \\\\ &\Rightarrow \Delta y=(x+\Delta x)^{\frac{1}{5}}-x^{\frac{1}{5}} \end{aligned}

Also,

        \begin{aligned} &\Delta y=f^{1}(x) \Delta x \\\\ &(x+\Delta x)^{\frac{1}{5}}-x^{\frac{1}{5}}=\frac{1}{5} x^{\frac{-4}{5}} \times \Delta x \end{aligned}

Put     x=32, \Delta x=1

        \begin{aligned} &(33)^{\frac{1}{5}}-(32)^{\frac{1}{5}}=\frac{1}{5}(2)^{4}(1) \\\\ &\Rightarrow(33)^{\frac{1}{5}}=2+0.0125=2.0125 \end{aligned}

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