Question

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

Answer 1

$$\begin{gathered} \mathrm{Let}: \\ x=\frac{\mathrm{\pi }}{2} \\ x+△x=\frac{22}{14} \\ \Rightarrow dx=△x=\frac{22}{14}-\frac{\mathrm{\pi }}{2}=0 \\ \mathrm{Now},y=\sin x \\ \Rightarrow \frac{dy}{dx}=\cos x \\ \Rightarrow {\left(\frac{dy}{dx}\right)}_{x=\frac{\mathrm{\pi }}{2}}=\cos \left(\frac{\mathrm{\pi }}{2}\right)=0 \\ \therefore ∆y=\frac{dy}{dx}∆x=0\times 0=0 \\ \Rightarrow △y=0 \end{gathered}$$

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