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August 21st, 2010, 01:15 AM   #1
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find the limit

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August 21st, 2010, 02:36 AM   #2
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Re: find the limit

I would do it like that

would be something like
then and then

but I guess I am completely wrong
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August 21st, 2010, 01:13 PM   #3
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Re: find the limit

you are completely wrong!
Since



(because the cosine function is less than 1 for every )
the limit is between 0 and 1.
Your application of rules for limits (and mathematics) is wrong - but nevertheless, I am
thinking about the right solution. It will be 1... and I hope someone is faster, since I
forgot a lot since studying physics.

Regards,
Jens
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August 21st, 2010, 01:13 PM   #4
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Re: find the limit

Let T = (cosx)^1/x^2 = exp[ln(cosx)/x^2].
As x ->0, cosx ~ 1 - x^2/2, so ln(cosx) ~ - x^2/2, therefore T ~ exp(-1/2).
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August 21st, 2010, 04:44 PM   #5
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Re: find the limit

It is my first time, and I worked on the answer, and It is:
1/Sqrt[e].
I hope it is the Right answer. Let me know if I am wrong.
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August 21st, 2010, 05:58 PM   #6
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Re: find the limit







l'Hopital's rule:



and again l'Hopital's:

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August 21st, 2010, 06:00 PM   #7
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Re: find the limit

right! Not a prove but indeed the right way to prove it, I guess. Sorry for the 1 posted.
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August 21st, 2010, 06:08 PM   #8
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Re: find the limit

my posting was with respect to mathman, l'Hospital is a perfect hit.
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