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cinar
Group Title
Let f be a continuous and bounded function on [a,b] such that if
 2 years ago
 2 years ago
cinar Group Title
Let f be a continuous and bounded function on [a,b] such that if
 2 years ago
 2 years ago

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satellite73 Group TitleBest ResponseYou've already chosen the best response.1
not really,but it kind of looks like a set up for integrating by parts
 2 years ago

cinar Group TitleBest ResponseYou've already chosen the best response.0
F'(x)=f(x) so we can say F'(t)=f(t) right..
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
that is what i was thinking, yes
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
maybe not exactly what you want, but you would get something like \(gF\int f g'\)
 2 years ago

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

cinar Group TitleBest ResponseYou've already chosen the best response.0
I guess enough to show that \[\int\limits f g'\] is convergent
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
first part is no problem, since \(\lim_{t\to \infty}g(t)=0\) and \(\int_a^\infty f(t)\) is bounded
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
yeah you hit the nail on the head, and frankly i don't see why that is true, so this might be the wrong approach
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
because all you know about \(g'\) is that \(g'\leq 0\)
 2 years ago

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
does this come in a section after some theorem or lemma that maybe you are supposed to use?
 2 years ago

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

satellite73 Group TitleBest ResponseYou've already chosen the best response.1
well then i guess this is the right approach!
 2 years ago
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