(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Calculate the limit:

[itex]lim_{(x,y)\rightarrow(0,0)}=\frac{4\sqrt{x^{14}+y^{14}}}{(x^{2}+y^{2})^{3}}[/itex]

3. The attempt at a solution

I think I'm supposed to use algebra for this but I can't seem to figure anything useful out.

I've found this:

[itex]x^{14}+y^{14}=(x^{2}+y^{2}) (x^{12}-x^{10} y^{2}+x^{8} y^{4}-x^{6} y^{6}+x^{4} y^{8}-x^{2} y^{10}+y^{12})[/itex]

but I'm not sure that helps me at all.

I know the limit exists and it's zero because I've plotted it.

Any help would be greatly appreciated.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Multivariable limit (x,y) to (0,0)

**Physics Forums | Science Articles, Homework Help, Discussion**