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Difficult Multivariate limit problem

  • Thread starter Scriabin11
  • Start date
  • #1

Homework Statement



I am supposed to show whether the limit:

lim (x,y)----> (0,0) of yln(x^2 + y^2) exists or doesn't.

Homework Equations





The Attempt at a Solution




I've tried numerous paths, but what it seems to come down to is showing that the y factor goes to zero quicker than the ln(x^2 +y^2) factor. And I don't believe L'Hopitals rule is applicable.
 

Answers and Replies

  • #2
L'hospitals rule is applicable since you end of with inderterminate forms when you approach x and y seperately.
 
  • #3
HallsofIvy
Science Advisor
Homework Helper
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In polar coordinates, [itex]y ln(x^2+ y^2)[/itex] becomes [itex]r sin(\theta) ln(r^2)= (2 r ln(r))sin(\theta)[/itex]. That will go to 0 independently of y if and only if [itex]\lim_{r\to 0} r ln(r)= 0[/itex]. Is that true?
 

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