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anonymous
 4 years ago
Let f be a continuous and bounded function on [a,b] such that if
anonymous
 4 years ago
Let f be a continuous and bounded function on [a,b] such that if

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anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0not really,but it kind of looks like a set up for integrating by parts

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0F'(x)=f(x) so we can say F'(t)=f(t) right..

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0that is what i was thinking, yes

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0maybe not exactly what you want, but you would get something like \(gF\int f g'\)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0\[\lim_{b \rightarrow} \int\limits_{0}^{b }G(t)F'(t)dt=\]

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0I guess enough to show that \[\int\limits f g'\] is convergent

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0first part is no problem, since \(\lim_{t\to \infty}g(t)=0\) and \(\int_a^\infty f(t)\) is bounded

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0yeah you hit the nail on the head, and frankly i don't see why that is true, so this might be the wrong approach

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0because all you know about \(g'\) is that \(g'\leq 0\)

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0does this come in a section after some theorem or lemma that maybe you are supposed to use?

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0no, this is homework, but prof gave the hint and said that you should use integration by part..

anonymous
 4 years ago
Best ResponseYou've already chosen the best response.0well then i guess this is the right approach!
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