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Two Path Test 
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#1
Feb2712, 03:48 PM

P: 63

1. The problem statement, all variables and given/known data
Use the two path test to prove that the following limits do not exist. 2. Relevant equations [tex]\lim_{(x,y)\rightarrow{(0,0)}}\frac{4xy}{3x^2+y^2}[/tex] 3. The attempt at a solution The book that I am using introduces the Two Path Test theoretically but does not show an example of how to do it, so I am a bit lost. Would I set x = y, and x = y? In some of the more basic problems I was able to set x = 0 and y = 0, and find the limits would differ, proving that there was no limit. But in this case, that's obviously not possible. 


#2
Feb2712, 03:51 PM

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Those two paths look like a good choice to me. Try them out. What's the limit along each path?



#3
Feb2712, 03:54 PM

P: 63




#4
Feb2712, 04:06 PM

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P: 25,246

Two Path Test



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