August 21st, 2010, 02:15 AM  #1 
Senior Member Joined: Aug 2010 Posts: 109 Thanks: 0  find the limit 
August 21st, 2010, 03:36 AM  #2 
Member Joined: Jul 2010 Posts: 95 Thanks: 0  Re: find the limit
I would do it like that would be something like then and then but I guess I am completely wrong 
August 21st, 2010, 02:13 PM  #3 
Member Joined: Aug 2010 Posts: 49 Thanks: 0  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 
August 21st, 2010, 02:13 PM  #4 
Global Moderator Joined: May 2007 Posts: 6,377 Thanks: 541  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). 
August 21st, 2010, 05:44 PM  #5 
Newbie Joined: Aug 2010 Posts: 17 Thanks: 0  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. 
August 21st, 2010, 06:58 PM  #6 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,637 Thanks: 959 Math Focus: Elementary mathematics and beyond  Re: find the limit l'Hopital's rule: and again l'Hopital's: 
August 21st, 2010, 07:00 PM  #7 
Member Joined: Aug 2010 Posts: 49 Thanks: 0  Re: find the limit
right! Not a prove but indeed the right way to prove it, I guess. Sorry for the 1 posted.

August 21st, 2010, 07:08 PM  #8 
Member Joined: Aug 2010 Posts: 49 Thanks: 0  Re: find the limit
my posting was with respect to mathman, l'Hospital is a perfect hit.


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