\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Write the order-1 limited expansion (\(DL_1\)) of \(f(x) = 1/(1 + x)\) at \(a = 0\) in the form \(f(0 + h) = f(0) + \ell h + h \, \varepsilon(h)\) with \(\varepsilon(h) \to 0\). Deduce \(f'(0)\).
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