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The problem is to either find the limit or show that it does not exist [tex]lim_{(x,y)\rightarrow(2,-2)}\frac{4-xy}{4+xy}[/tex]

I've been able to do similar problems to this such as

[tex]lim_{(x,y)\rightarrow(0,0)}\frac{xy}{x^2+y^2}[/tex] where I took two different paths to the limit and found that they were not equal and so it didn't exist. However, for this one I can't seem to pick a function that gives me a limit that exists let alone two functions that give me two different limits.

I've tried coming from the following paths for the problem

[tex]y=-x[/tex]

[tex]y=x-4[/tex]

[tex]y=-2[/tex]

[tex]y=x^2-6[/tex]

[tex]x=2[/tex]

No matter which one I do I can't seem to get anything to cancel out in order to simplify it to one that I can perform the limit on. Are there two functions that I can use to get this limit and how would I find these. If there aren't then how would I prove that this limit exists?

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# Homework Help: Stuck Proving a Limit Doesn't exist

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