Question

If y = log_e x, then find ∆y when x = 3 and ∆x = 0.03.

Answer 1

We have

$$\begin{gathered} x=3 \\ ∆x=0.03 \\ y={\log }_{e}x \\ \mathrm{For}x=3, \\ y={\log }_{e}3 \\ \mathrm{Also},\frac{dy}{dx}=\frac{1}{x} \\ \Rightarrow {\left(\frac{dy}{dx}\right)}_{x=3}=\frac{1}{3} \\ \Rightarrow ∆y=dy=\frac{dy}{dx}dx=\frac{1}{3}\times 0.03=0.01 \end{gathered}$$