Lim x^2-4y^2/(x+2y) as (x,y)->(-2,1): -4 or DNE?

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SUMMARY

The limit of the expression (x^2 - 4y^2)/(x + 2y) as (x,y) approaches (-2,1) does not exist (DNE). This conclusion is reached because the expression is undefined along the line x + 2y = 0. The limit can be simplified to x - 2y for values where x is not equal to -2y, but at the point (-2,1), the limit fails to converge to a specific value.

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lim (x^2-4y^2)/(x+2y) as (x,y)->(-2,1)
Does this limit go to -4 or DNE since it is undefined all along x+2y?
 
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It Does Not Exist.
 
Please note that you may write this as:
[tex]\frac{x^{2}-4y^{2}}{x+2y}=\frac{(x-2y)(x+2y)}{x+2y}=x-2y,x\neq{-}2y[/tex]
 

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