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0606 P22 - Mar 2019 - Q2 - 6 marks
8242

Variables \(x\) and \(y\) are related by the equation \(y=\dfrac{\ln x}{e^x}\).

(i) Show that \(\dfrac{dy}{dx}=\dfrac{1-\ln x}{xe^x}\).

(ii) Hence find the approximate change in \(y\) as \(x\) increases from \(2\) to \(2+h\), where \(h\) is small.

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