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December 4th, 2009, 10:02 PM  #1 
Member Joined: Dec 2006 Posts: 90 Thanks: 0  Continuity of multivariable functions
For what values of the number is the following function continuous on ? 
December 5th, 2009, 04:47 PM  #2 
Global Moderator Joined: May 2007 Posts: 6,008 Thanks: 440  Re: Continuity of multivariable functions
Your latex expressions aren't working!

December 5th, 2009, 08:17 PM  #3 
Member Joined: Dec 2006 Posts: 90 Thanks: 0  Re: Continuity of multivariable functions
For what values of the number a is the following function continuous on R^3? f(x,y,z)=((x+y+z)^a)/(x^2+y^2+z^2) if (x,y,z)=/ 0 f(x,y,z)=0 if (x,y,z)= 0 
December 6th, 2009, 02:27 PM  #4  
Global Moderator Joined: May 2007 Posts: 6,008 Thanks: 440  Re: Continuity of multivariable functions Quote:
If a is an integer, then a>2 is obviously needed for continuity. At a=2, it looks like the expression is undefined. Examples: x=y=0, let z>0 then f > 1. z=0, x=y, let x > 0 then f> 2. I suspect for a > 2, noninteger, you will have continuity, while for a < 2, f will blow up. You might try L'Hopital's rule to prove these.  
December 7th, 2009, 01:25 AM  #5 
Global Moderator Joined: Dec 2006 Posts: 15,326 Thanks: 1016 
The reason why latex was not interpreted was that bigli had selected the "Disable BBCode" option.

December 10th, 2009, 09:08 PM  #6 
Member Joined: Dec 2006 Posts: 90 Thanks: 0  Re: Continuity of multivariable functions
For what values of the number is the following function continuous on ? 

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