If y = sin x and x changes from π/2 to 22/14,

Question:

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

Solution:

Let:

$x=\frac{\pi}{2}$

$x+\Delta x=\frac{22}{14}$

$\Rightarrow d x=\Delta x=\frac{22}{14}-\frac{\pi}{2}=0$

Now, $y=\sin x$

$\Rightarrow \frac{d y}{d x}=\cos x$

$\Rightarrow\left(\frac{d y}{d x}\right)_{x=\frac{x}{2}}=\cos \left(\frac{\pi}{2}\right)=0$

$\therefore \Delta y=\frac{d y}{d x} \Delta x=0 \times 0=0$

$\Rightarrow \triangle y=0$

Hence, there is no change in the value of y.

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