Let \(u_n(t)\), \(n=1,2…\) be a sequence of concave functions on \(\mathbb{R}\). Let \(g(t)\) be a differentiable function on \(\mathbb{R}\). Assume \(\liminf_{n\to\infty} u_n(t) \geq g(t)\) for every \(t\) and \(\lim_{n\to \infty} u_n(0) = g(0)\). Suppose \(u_n'(0)\) exist for \(n=1,2,…\). Compare \(\lim_{n\to \infty} u_n'(0)\) and \(g'(0)\).

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