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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.

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

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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 $\frac{1}{2}$.

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  • $\begingroup$ Good enough. +1 $\endgroup$
    – Mark Viola
    Sep 20, 2015 at 18:41

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