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Let $$f(x) = \sin x, g(x) = x$$. Statement 1: $$f(x) \leq g(x)$$ for $$x$$ in $$(0, \infty)$$ Statement 2: $$f(x) \leq 1$$ for $$x$$ in $$(0, \infty)$$ but $$g(x) \to \infty$$ as $$x \to \infty$$.
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