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As the topic, Use $\epsilon $-$ \delta$ definition to prove $\lim\limits_{(x,y)\rightarrow (0,0)} \frac{(xy)^4}{ (x^2 + y^4)^3}$ exists. I tried to use the inequalities $|x+y|>|xy|$ and $x^2+y^4>(xy^2)$ but I am not not sure how to set up the inequality only with $|x+y|^n<\delta ^n< \epsilon$

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    Ok, let us $\varepsilon >0$...2012-10-21

3 Answers 3