Lim (x^2-4y^2)/(x+2y) as (x,y)->(-2,1)

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The limit of the expression (x^2 - 4y^2)/(x + 2y) as (x, y) approaches (-2, 1) does not exist (DNE) due to the undefined nature of the denominator along the line x + 2y = 0. The discussion emphasizes the importance of understanding the definition of limits in multivariable calculus to support conclusions. Participants agree that the limit cannot be evaluated directly at the point of interest.

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Dustinsfl
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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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You mean x+2y=0, right? You seem to know exactly what the problem is. My inclination is to say, no, does not exist. But you might want to look up the exact phrasing of the definition of limit to be sure. Then you'll be prepared to defend it in court.
 

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