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  • Please solve RD Sharma class 12 chapter 13 Differentials Errors and Approximations exercise multiple choice question 13 maths textbook solution

Please solve RD Sharma class 12 chapter 13 Differentials Errors and Approximations exercise multiple choice question 13 maths textbook solution

Answers (1)

Answer: (a) 0.32

Hint: Here we use the basic concept of x=x+\Delta x

Given: y=x^{4}-10

Solution:

Let  x=1.99

So  

      \begin{aligned} &x+\Delta x=2 \\ &\Delta x=2-1.99=0.01 \end{aligned}

Let

        \begin{gathered} d x=\Delta x=0.01 \\ y=x^{4}-10 \end{gathered}

Let’s differentiate,

        \begin{aligned} &y=x^{4}-10 \\\\ &\frac{d y}{d x}=4 x^{3} \end{aligned}

        \left(\frac{d y}{d x}\right)_{x=2}=4(2)^{3}=32

\therefore \quad \frac{d y}{d x} \times d x=d y

So,        d y=32(0.01)=0.32(\text { approx })

So, approximate change in y =0.32

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