Question

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

Answer 1

We have

\[x = 3\]

\[ ∆ x = 0 . 03\]

\[y = \log_e x\]

\[\text { For } x = 3, \]

\[y = \log_e 3\]

\[\text { Also }, \frac{dy}{dx} = \frac{1}{x}\]

\[ \Rightarrow \left( \frac{dy}{dx} \right)_{x = 3} = \frac{1}{3}\]

\[ \Rightarrow ∆ y = dy = \frac{dy}{dx}dx = \frac{1}{3} \times 0 . 03 = 0 . 01\]