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

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

Answers (1)

Answer:  3.9961

Hint:  Here, we use the formula

        \Delta y=f(x+\Delta x)-f(x)

Given: (255)^{\frac{1}{4}}

Solution: 

Let  y=x^{\frac{1}{4}}=(256)^{\frac{1}{4}}=4

where x=16

\begin{aligned} &x+\Delta x=255 \\\\ &\Delta x=-1 \end{aligned}

Now, y=x^{\frac{1}{4}}

Differentiating w.r.t x

\frac{d y}{d x}=\frac{1}{4} x^{\frac{-3}{4}}

Using,

\Delta y=\frac{d y}{d x} \Delta x=\frac{1}{4 x^{\frac{3}{4}}} \times-1

Putting the value of x

\begin{aligned} &\Delta y=\frac{-1}{4(256)^{\frac{3}{4}}}=\frac{-1}{4 \times 4^{4 \times \frac{3}{4}}}=\frac{-1}{256}=-0.0039 \\\\ &(255)^{\frac{1}{4}}=y+\Delta y \end{aligned}

                \begin{aligned} &=4+(-0.0039) \\\\ &=3.9961 \end{aligned}

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