\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Show that \(\ln(1 + x) \le x - \frac{x^2}{2} + \frac{x^3}{3}\) for every \(x \ge 0\), and \(\ln(1+x) \ge x - x^2/2\) for \(x \ge 0\).
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