If y= and x changes from 2 to 22 14 , what is the approximate cha… - Vidyadip

Question

If $\text{y}=\sin\text{x}$ and x changes from $\frac{\pi}{2}$ to $\frac{22}{14}$, what is the approximate change in y?

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Answer

Let:
$\text{x}=\frac{\pi}{2}$
$\text{x}+\triangle\text{x}=\frac{22}{14}$
$\Rightarrow\text{dx}=\triangle\text{x}=\frac{22}{14}=\frac{\pi}{2}=0$
Now, $\text{y}=\sin\text{x}$
$\Rightarrow\frac{\text{dy}}{\text{dx}}=\cos\text{x}$
$\Rightarrow\Big(\frac{\text{dy}}{\text{dx}}\Big)_{\text{x}=\frac{\pi}{2}}=\cos\Big(\frac{\pi}{2}\Big)=0$
$\therefore\ \triangle\text{y}=\frac{\text{dy}}{\text{dx}}\Rightarrow\triangle\text{y}=0\text{x}=0\times0=0$
$\Rightarrow\triangle\text{y}=0$

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