# Multivariable Limit - Squeeze Theorem

I was trying to prove that this limit exists, but I cannot use Polar coordinates. Is there a special inequality that I can use along with the Squeeze Theorem to show that it does indeed equal $0$? Thanks.

$$\lim_{(x,y)\to(0,0)}\dfrac{(x^5y^2)}{(x^{10} + y^4)}.$$

• This is just a substitution away from the standard $xy/(x^2+y^2)$ problem.
– zhw.
Sep 20 '15 at 17:55
• Dec 3 '19 at 16:24

The limit doesn't exist. For instance, in the $x$-axis you always have $0$, but if on the curve $y=x^{\frac{5}{2}}$ you have always $\frac{1}{2}$.