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4. Suppose f(x) is a continuous function on [0,â) and f(x) > 0 for all x â [0,â). Let
ô° x tf(t)dt 0
g(x) = ô° x . Show that 0 f(t)dt
(1) lim g(x) = 0, and xâ0+
1
(2) g(x) is increasing on (0, â).