I'm trying to verify that: [tex]\lim_{(x,y)\rightarrow (0,0)}\frac{\sin (x^{3}+y^{3})}{x+y^{2}}=0.[/tex](adsbygoogle = window.adsbygoogle || []).push({});

[tex]0<\sqrt{x^2+y^2}<\delta\rightarrow |\frac{\sin (x^{3}+y^{3})}{x+y^{2}}|<\epsilon[/tex]

[tex]0\leq |\sin (x^{3}+y^{3})|\leq |(x^{3}+y^{3})|\leq |x|x^2+|y|y^2[/tex]

[tex]|\frac{\sin (x^{3}+y^{3})}{x+y^{2}}|\leq \frac{ |x|x^2+|y|y^2}{|x+y^{2}|}[/tex]

So I'm stuck here because of the denominator |x+y²|. What can I do?

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# I Limit of a two variable function

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