show using the inequality that
i know bernoullis inequality is
but i'm not seeing how i can prove the above one using this one here
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will'o'wisp2
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- 12-11-2017 15:47
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RDKGames
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- 12-11-2017 16:14
(Original post by will'o'wisp2)
show using the inequality that
i know bernoullis inequality is
but i'm not seeing how i can prove the above one using this one herefor
and
Now work with this. -
will'o'wisp2
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- 12-11-2017 16:46
(Original post by RDKGames)
Gonna replace the variables in the ineq. and say thatfor
and
Now work with this.but i'm not sure about the right hand side
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- 12-11-2017 16:49
(Original post by will'o'wisp2)
so the left hand side i can make 1+1/x in the form 1+rx by saying thatbut i'm not sure about the right hand side
and
(for
) in order to get
on the LHS. Then the RHS just falls out.
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- 12-11-2017 16:58
(Original post by RDKGames)
Rather than doing whatever you tried to do here, I'd recommend picking appropriateand
(for
) in order to get
on the LHS. Then the RHS just falls out.
so i thought about 0.5 which is like to the power of 1/2 which is great but how do i do 1/x? -
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- 12-11-2017 17:00
(Original post by will'o'wisp2)
so i picked y=1 which gives me 2 but i can't think of an r within 0 and 1 inclusive so that r = 1/x i just can't find one
so i thought about 0.5 which is like to the power of 1/2 which is great but how do i do 1/x?is fine, but is
what you're looking for to substitute. Agree?
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- 12-11-2017 17:03
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- 12-11-2017 17:04
(Original post by will'o'wisp2)
uh ye, so r= 0.x? -
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- 12-11-2017 17:06
(Original post by RDKGames)
Huh? -
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- 12-11-2017 17:07
(Original post by will'o'wisp2)
what am i doing with r?in the inequality, obviously.
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- 12-11-2017 17:11
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- 12-11-2017 17:15
(Original post by will'o'wisp2)
uh so i just get out what i question originally says, so is that the proof? finding values of y and r such that you can make the inequality in the original question?such that, for
,
and
thus satisfying Bernoulli's requirements for it to hold true, so your result must hold true. Since your result is what you're asked to prove, then well... you've proven it.
There might be a different approach but this one works out quite nicely.Last edited by RDKGames; 12-11-2017 at 17:16. -
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- 12-11-2017 17:20
(Original post by RDKGames)
You've used a proven result (Bernoulli's ineq.) to show the proposed result by picking appropriatesuch that, for
,
and
thus satisfying Bernoulli's requirements for it to hold true, so your result must hold true. Since your result is what you're asked to prove, then well... you've proven it.
There might be a different approach but this one works out quite nicely. -
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- 12-11-2017 17:32
(Original post by will'o'wisp2)
ah ok coolio, thanks man
Bernoulli's inequality isfor
and
.
Pick, then
which is true by the above theorem.
Then doingmeans
if
which leads us to the condition that the statement is true only if ....?
And just finish it off by stating the condition onfrom solving
Perhaps you're more comfortable with this approach.Last edited by RDKGames; 12-11-2017 at 17:34. -
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- 12-11-2017 21:22
(Original post by RDKGames)
You may also prove it by saying that:
Bernoulli's inequality isfor
and
.
Pick, then
which is true by the above theorem.
Then doingmeans
if
which leads us to the condition that the statement is true only if ....?
And just finish it off by stating the condition onfrom solving
Perhaps you're more comfortable with this approach.
i don't understand where the 1+ x multiplied by 1/x comes from -
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- 12-11-2017 21:50
(Original post by will'o'wisp2)
https://cdn.discordapp.com/attachmen...05/unknown.png
i don't understand where the 1+ x multiplied by 1/x comes fromis Bernoulli's so let
and
which gives the result.
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- 12-11-2017 21:52
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