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

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SUMMARY

The discussion focuses on applying the Delta-Epsilon proof to demonstrate the limit of the function (y^3 + 5x^2y)/(y^2 + 3y^2) as (x,y) approaches (0,0). Participants express confusion regarding the presence of the cubic term y^3, contrasting it with previous examples that predominantly featured squared terms. Clarification is sought on the correctness of the denominator, specifically the expression "y^2 + 3y^2". The consensus is that the limit exists and can be proven using the Delta-Epsilon method.

PREREQUISITES
  • Understanding of Delta-Epsilon definitions in calculus
  • Familiarity with multivariable limits
  • Knowledge of polynomial functions and their behavior near limits
  • Basic algebraic manipulation skills
NEXT STEPS
  • Study the Delta-Epsilon definition for multivariable limits in detail
  • Practice additional examples of Delta-Epsilon proofs involving cubic terms
  • Explore the implications of different polynomial degrees on limit behavior
  • Review common pitfalls in multivariable limit proofs
USEFUL FOR

Students and educators in calculus, particularly those focusing on multivariable functions and limit proofs, as well as anyone seeking to strengthen their understanding of Delta-Epsilon arguments.

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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