MHB [Limits] Help with Delta-Epsilon Proofs for Multivariable Functions

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The discussion focuses on applying Delta-Epsilon proofs to establish the limit of the function (y^3 + 5x^2y)/(y^2 + 3y^2) as (x,y) approaches (0,0). The user expresses confusion regarding the presence of the cubic term y^3, which differs from previous examples that primarily featured squared terms. Additionally, there is uncertainty about the denominator, specifically the expression "y^2 + 3y^2," which raises questions about its correctness. Participants are encouraged to clarify the problem and assist with the proof. The conversation highlights the challenges of multivariable limit proofs and the importance of correctly interpreting mathematical expressions.
Steve1231
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Hi guys, just having some confusions on the Delta-Epsilon proofs for multivariable limit functions.
here is my question:

Apply Delta-Epsilon proof for the Lim (x,y) --> (0,0) of (y^3 + 5x^2y)/(y^2 + 3y^2) to show the limit exists.
The part that has me confused is the y to the power of 3, where as most of the examples I've worked through thus far only contain squared variables.
Any help is appreciated =)
 
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The "y^2 + 3y^2" in the denominator seems odd. Are you sure the problem is typed properly?
 

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