\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Show that the family \((x \mapsto e^{a x})_{a \in \mathbb{R}}\) of \(C(\mathbb{R}, \mathbb{R})\) is free, by an asymptotic study as \(x \to +\infty\).
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