June 4th, 2012, 03:24 PM  #1 
Senior Member Joined: Jan 2012 Posts: 159 Thanks: 0  As The Limit Goes To Infinity... taking the conjugate of the numerator seems long, am I missing something? 
June 4th, 2012, 06:23 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: As The Limit Goes To Infinity...
We are given: I would write: Now we have: Which is the the indeterminate form 0/0, thus L'Hôpital's rule gives (after simplification): 
June 4th, 2012, 06:56 PM  #3 
Senior Member Joined: Jan 2012 Posts: 159 Thanks: 0  Re: As The Limit Goes To Infinity...
Is there a way to solve without L'Hôpital's rule? I am just studying past tests but our teach said we cannot use L'Hôpital's rule but maybe previous years could... Dunno

June 4th, 2012, 07:57 PM  #4 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,211 Thanks: 520 Math Focus: Calculus/ODEs  Re: As The Limit Goes To Infinity...
Okay, barring the use of our good friend L'Hôpital, we could complete the square under the radicals to get: Now, we may observe that: where hence: thus, we have: 
June 4th, 2012, 08:11 PM  #5 
Senior Member Joined: Jan 2012 Posts: 159 Thanks: 0  Re: As The Limit Goes To Infinity...
nice mark I tried completing the square but made a simple mistake! At least I was headed in the right direction.


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