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June 7th, 2011, 05:30 AM   #1
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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,
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June 7th, 2011, 05:58 AM   #2
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Re: How can I solve this limit problem

What happens when y = x?
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June 7th, 2011, 08:30 AM   #3
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Re: How can I solve this limit problem

Quote:
Originally Posted by The Chaz
What happens when y = x?
Then the limit will be =2 ? right?

thanks,
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June 7th, 2011, 03:18 PM   #4
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Re: How can I solve this limit problem

Quote:
Originally Posted by abdlaziz
Quote:
Originally Posted by The Chaz
What happens when y = x?
Then the limit will be =2 ? right?

thanks,
On the other hand when y = -x, the limit =0. So it seems it is discontinuous at x=y=0.
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June 7th, 2011, 04:26 PM   #5
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Using the l'H˘pital's rule twice,
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June 8th, 2011, 08:33 AM   #6
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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 y-x 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.
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June 8th, 2011, 09:22 AM   #7
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Re: How can I solve this limit problem

Welcome (back) to the forum, HallsofIvy!

Also, it's "The Chaz"
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