June 7th, 2011, 05:30 AM  #1 
Newbie Joined: Jun 2011 Posts: 2 Thanks: 0  How can I solve this limit problem
Hi, How can I solve this problem Limit of (x+y)^2/(x^2+y^2)as (x,y) approaches (0,0)? Thank, 
June 7th, 2011, 05:58 AM  #2 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: How can I solve this limit problem
What happens when y = x?

June 7th, 2011, 08:30 AM  #3  
Newbie Joined: Jun 2011 Posts: 2 Thanks: 0  Re: How can I solve this limit problem Quote:
thanks,  
June 7th, 2011, 03:18 PM  #4  
Global Moderator Joined: May 2007 Posts: 6,786 Thanks: 708  Re: How can I solve this limit problem Quote:
 
June 7th, 2011, 04:26 PM  #5 
Senior Member Joined: Apr 2007 Posts: 2,140 Thanks: 0 
Using the l'Hôpital's rule twice, 
June 8th, 2011, 08:33 AM  #6 
Math Team Joined: Sep 2007 Posts: 2,409 Thanks: 6  Re: How can I solve this limit problem
How did you apply L'Hopital's rule? What did you differentiate with respect to? As The Chas pointed out, when y= x, this becomes 4x^2/2x^2= 2 but when yx it becomes 0/x^2= 0. That is, the limit is 2 approached along the line y= x but 0 approached along the line y= x. The limit must be the same when approached along any line so this limit does not exist. 
June 8th, 2011, 09:22 AM  #7 
Global Moderator Joined: Nov 2009 From: Northwest Arkansas Posts: 2,766 Thanks: 4  Re: How can I solve this limit problem
Welcome (back) to the forum, HallsofIvy! Also, it's "The Chaz" 

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