For each ofthe two functions i on [1, 00) defined below, show that limn -+ 00 i; i exists while i is not integrable over [1, 00). does this contradict the continuity of integration? (i) define i(x) = (-inn, forn: s x < n + 1. (ii) define i(,t) = (sinx )/x for 1 : s x < 00.

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