\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Show that the family \((x \mapsto e^x, x \mapsto e^{2x}, x \mapsto e^{x^2})\) is free (i.e.\ linearly independent) in \(\mathbb{R}^\mathbb{R}\)
  1. by an asymptotic study as \(x \to +\infty\);
  2. by evaluation at well-chosen points.

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