7. (a) Suppose that f is improperly integrable on [0,00). Prove that if L limx->oo f(x) exists,...
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7.
(a) Suppose that f is improperly integrable on [0,00). Prove that if L limx->oo f(x) exists, then L = O.
(b) Let f(x) = { ~ n::; x < n + 2-n , n E N otherwise.
Prove that f is improperly integrable on [0,00) but limx->oo f(x) does not exist.
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