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Proof needed -- Convergence
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Jack
Jan 30, 2013, 3:56:37 PM1/30/13
to
Can anyone show me a good way to prove that
lim_(x->oo)
(ln(x + ln(x))) / ((x+ln(x))*(ln(x + ln(x)) - ln(x)))
= 1
?
With thanks in advance.
lim_(x->oo)
(ln(x + ln(x))) / ((x+ln(x))*(ln(x + ln(x)) - ln(x)))
= 1
?
With thanks in advance.
Frederick Williams
Jan 30, 2013, 4:58:19 PM1/30/13
to
--
When a true genius appears in the world, you may know him by
this sign, that the dunces are all in confederacy against him.
Jonathan Swift: Thoughts on Various Subjects, Moral and Diverting
Jack
Jan 30, 2013, 5:34:38 PM1/30/13
to
"Frederick Williams" <freddyw...@btinternet.com> wrote in message
news:5109977B...@btinternet.com...
> Jack wrote:
>>
>> Can anyone show me a good way to prove that
>>
>> lim_(x->oo)
>>
>> (ln(x + ln(x))) / ((x+ln(x))*(ln(x + ln(x)) - ln(x)))
>> = 1
>> ?
>>
>> With thanks in advance.
>
> Is it true?
>
According to Wolfram Alpha it is. I asked it to do its trick of showing the
>>
>> Can anyone show me a good way to prove that
>>
>> lim_(x->oo)
>>
>> (ln(x + ln(x))) / ((x+ln(x))*(ln(x + ln(x)) - ln(x)))
>> = 1
>> ?
>>
>> With thanks in advance.
>
> Is it true?
>
steps but it said that they were unavailable this time. Perhaps it didn't
know how it did it :-).
Jack
Jan 31, 2013, 2:36:52 PM1/31/13
to
Do you think it *needs* proving that
lim_(x --> oo)} (ln(x) / x) / (ln(x + ln(x)) - ln(x)) = 1
(which is the central result in respect to the convergence I've been asking
about) or can it be taken to be true without proof? After all, the
calculator says it's true....
lim_(x --> oo)} (ln(x) / x) / (ln(x + ln(x)) - ln(x)) = 1
(which is the central result in respect to the convergence I've been asking
about) or can it be taken to be true without proof? After all, the
calculator says it's true....
Frederick Williams
Jan 31, 2013, 5:38:16 PM1/31/13
to
L'Hopital's rule.
Frederick Williams
Jan 31, 2013, 5:38:22 PM1/31/13
to
Jack wrote:
>
> Do you think it *needs* proving that
>
> lim_(x --> oo)} (ln(x) / x) / (ln(x + ln(x)) - ln(x)) = 1
Spurious '}'.
>
> Do you think it *needs* proving that
>
> lim_(x --> oo)} (ln(x) / x) / (ln(x + ln(x)) - ln(x)) = 1
>
> (which is the central result in respect to the convergence I've been asking
> about) or can it be taken to be true without proof? After all, the
> calculator says it's true....
Jack
Jan 31, 2013, 10:05:58 PM1/31/13
to
news:510AF258...@btinternet.com...
> Jack wrote:
>>
>> Do you think it *needs* proving that
>>
>> lim_(x --> oo)} (ln(x) / x) / (ln(x + ln(x)) - ln(x)) = 1
>>
>> (which is the central result in respect to the convergence I've been
>> asking
>> about) or can it be taken to be true without proof? After all, the
>> calculator says it's true....
>
> For a human proof of the above or the original you may wish to try
> L'Hopital's rule.
>
Thanks -- I got it in the end, after signing up for Wolfram Alpha Pro.
>>
>> Do you think it *needs* proving that
>>
>> lim_(x --> oo)} (ln(x) / x) / (ln(x + ln(x)) - ln(x)) = 1
>>
>> (which is the central result in respect to the convergence I've been
>> asking
>> about) or can it be taken to be true without proof? After all, the
>> calculator says it's true....
>
> For a human proof of the above or the original you may wish to try
> L'Hopital's rule.
>
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