Disprove or prove using delta-epsilon definition of limit that $\lim_{(x,y) \to (0,0)}{\frac{x^3-y^3}{x^2-y^2}} = 0$

So, you've reduced it to $\frac{x^2+xy+y^2}{x+y}$. That denominator is zero at more than just the origin $(0,0)$. What happens on (or close to) the line $y=-x$?


Hint: Try something close to the forbidden lines $x^2=y^2,$ like $y=x^3-x.$

Tags:

Limits

Real Analysis

Multivariable Calculus

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