(Solution) - A Prove that converges uniformly on b Prove that 0 e xydx -(2025 Original AI-Free Solution)

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a) Prove that

converges uniformly on (-?,?).
b) Prove that ?0? e-xydx converges uniformly on [1, ?).
c) Prove that ?0? ye-xydx exists for each y ? [0, ?) and converges uniformly on any [a, b] ? (0, ?) but that it does not converge uniformly on [0, 1].