If y = _e x, then find when x = 3 and = 0.03. - Vidyadip

Question

If $y = \log_e x$, then find $\triangle\text{y}$ when $x = 3$ and $\triangle\text{x} = 0.03.$

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Answer

Here
$\text{x}=3,\triangle\text{x}=0.030\ \text{and}\ \text{y}=\log_\text{e}\text{x}$
$\frac{\text{dy}}{\text{dx}}=\frac{1}{\text{x}}$
$\Big(\frac{\text{dy}}{\text{dx}}\Big)_{\text{x}-3}=\frac{1}{3}$
$\triangle\text{y}=\Big(\frac{\text{dy}}{\text{dx}}\Big)_{\text{x}-3}\text{x}(\triangle\text{x})$
$=\Big(\frac{1}{3}\Big)(0.03)$
$\triangle\text{y}=0.01$

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