Two-variable calculus

  • Thread starter superdave
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  • #1
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Homework Statement



Show that the following limit does not exist:

lim (x,y) --> (0,0) of x^2 / (y^2 + x^2)

Homework Equations





The Attempt at a Solution



I think it involves using l'hospitals rule and using partial derivatives, but I really don't know.
 

Answers and Replies

  • #2
Office_Shredder
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For a limit to exist in multiple dimensions, it must be the same no matter which path you approach the point from. So if (x,y) travels over, say, y=x to (0,0), if the limit exists, it must be the same as if (x,y) travels over y=0 to (0,0).

So try two paths, show the limit is different depending on how you approach (0,0), and you're done
 
  • #3
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I'm not really sure how to go about that
 
  • #4
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I know how to take partial derivatives and directional derivatives...
 
  • #5
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Set y=x, and see what the limit is when x->0. Then try setting y=0, and see what the limit is as x->0. This is the idea for proving any limit in multiple variables does not exist, just go along different lines, if you get different answers, the limit does not exist.
 
  • #6
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Ah, I ge tit now, thanks
 

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