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Question
If y = loge x, then find ∆y when x = 3 and ∆x = 0.03 ?
Solution
We have
\[x = 3\]
\[ ∆ x = 0 . 03\]
\[y = \log_e x\]
\[\text { For } x = 3, \]
\[y = \log_e 3\]
\[\text { Also }, \frac{dy}{dx} = \frac{1}{x}\]
\[ \Rightarrow \left( \frac{dy}{dx} \right)_{x = 3} = \frac{1}{3}\]
\[ \Rightarrow ∆ y = dy = \frac{dy}{dx}dx = \frac{1}{3} \times 0 . 03 = 0 . 01\]
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