Suppose that ƒ is continuous and F(x) = g> 0, g'>0 and integrable on [a, b) and that lim g(x) = I-b- 1 lim g(2) f(t)g(1) dt = 0, r>1. f(t) dt is bounded on [a,b). Moreover, we let = ∞o. Show that

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