Im triying to explain this delta-epsilon problem, but I didnt find a way to attack effectively this rigorous demonstration enter image description here

I actually i tried a lot of inequalities (Cauchy-Schwarz etc), but nothing came up with this demostration, Im stuck here, its a difficult solution or Im just dump??

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    $\begingroup$ I agree that this is better suited to math.stackexchange.com. However, a hint: this expression can be rewritten as $\frac{2(x+3)^3+5(y-4)^3}{\sqrt{(x+3)^2+(y-4)^2}}$. $\endgroup$ – Steven Gubkin Jun 28 '17 at 13:45
  • $\begingroup$ Agree Steven Im changing to MathSE. thank for your comment $\endgroup$ – Wilfred V Jun 28 '17 at 16:58

Welcome to SE. As you are asking on a side for math educators, I assume that you want to explain this to students. My advice: don't. Start with much, much easier examples to get the students accustomed to such problems, then come back to it later; if at all.

If you, as the teacher/professor, are not able to find a solution for this problem, it is too hard for students who are new to the topic.

Furthermore, you have to really understand all the concepts behind it. Therefore, reciting an answer you might get here on how to do it might not be convincing and thus bad for your students.

In case that this is a homework problem or you are looking for how to answer it for different reasons than teaching it, you might want to try at Math.SE.

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    $\begingroup$ Indeed I want to solve in order to explain it, I understand the concept behind the whole limit idea, its just about the technic and manipulation. But Im think agree with you that it could be more suited for Math SE. But Thanks for your orientation. $\endgroup$ – Wilfred V Jun 28 '17 at 16:54

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