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

Answers (1)

Answer: 1

Hint: here we use, f(x+\Delta x)-f(x)

Given:   \sin \left(\frac{12}{14}\right)

Solution:  Let y=f(x)=\sin 2 x

\begin{aligned} &\text { Let: } x=\frac{22}{7} \\\\ &x+\Delta x=\frac{22}{14} \\\\ &\text { Then, } \Delta x=\frac{-22}{14} \\\\ &\text { For } x=\pi \end{aligned}

\begin{aligned} &y=\sin \left(\frac{22}{7}\right)=0 \\\\ &\text { Let: } d x=\Delta x=\sin \frac{-22}{14}=-\sin \left(\frac{\pi}{2}\right) \\\\ &\text { Now, } y=\sin 2 x\end{aligned}

\begin{aligned} &\frac{d y}{d x}=\cos 2 x \\\\ &\left(\frac{d y}{d x}\right)_{x=\frac{22}{7}}=-1 \end{aligned}

\begin{aligned} &\Delta y=d y=\frac{d y}{d x} d x=-1 \times-1=1 \\\\ &\Delta y=1 \\\\ &\sin \frac{22}{14}=y+\Delta y=1 \end{aligned}

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