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  • Need solution for RD Sharma maths class 12 chapter Differentials Errors and Approximations exercise 13.1 question 11

Need solution for RD Sharma maths class 12 chapter Differentials Errors and Approximations exercise 13.1 question 11

Answers (1)

Answer: 34.495

Hint: Here we use this below formula

\Delta y=f(x+\Delta x)-f(x)

Given:  x^{3}-7 x^{2}+15

Solution:  x=5 \Delta x=0.001

⇒ then we have,

\begin{aligned} &f(5.001)=f(x+\Delta x)=(x+\Delta x)^{2}-7(x+\Delta x)^{2} \\ &=f 15 \end{aligned}

Now,   \Delta y=f(x+\Delta x)-f(x)

\begin{aligned} &\therefore f(x+\Delta x)=f(x)+\Delta y \\\\ &=f(x)+f(x) \Delta x \\\\ &\Rightarrow f(5.001)=\left(x^{3}-7 x^{2}+15\right)+\left(3 x^{2}-14 x\right) \Delta x \\\\ &=\left[(5)^{3}-7(5)^{2}+15\right]+\left[3(5)^{2}-14(5)\right](0.001) \end{aligned}

\begin{aligned} &=-35+(s)(0.001) \\\\ &=-35+0.005 \\\\ &=-34.995 \end{aligned}

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