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[b]1. The problem statement, all variables and given/known data[/b]A

  • Thread starter wimma
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  • #1
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Homework Statement


A few:
(1) lim(x,y) -> (0,0) of (x^4*y^2)/(x^2 + y^2)2
(2) lim(x,y) -> (0,0) of x^4 / (y+x^2)

Homework Equations





The Attempt at a Solution


(1) i get that it exists and equals 0 by using polar coordinates
(2) i get that it exists (except for the parabolic path y=-x^2) and equals zero [using (t, mt) and (t, mt^2)]
 
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Answers and Replies

  • #2
Dick
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1) looks fine. For 2) how can you have a limit 'except for' something? Look at the path x=t, y=(-t^2). Just because the limit exists on some paths doesn't prove anything.
 
  • #3
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yeah but the question says "please ignore the parabolic path y=-x^2" :)
 
  • #4
Dick
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Since the denominator vanishes on that path, what do you think happens very close to that path?
 

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