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

Prove: [tex]lim_{(x,y)\rightarrow (0.0)} \frac{x^4 y}{x^4 + y^2} = 0[/tex]

2. Relevant equations

x = rcos(theta)

y= rsin(theta)

3. The attempt at a solution

since (x,y) are at the origin, I could use polar coordinates

[tex]lim_{(x,y)\rightarrow (0.0)} \frac{x^4 y}{x^4 + y^2} = lim_{(r)\rightarrow 0} \frac{r^4 cos^4 \vartheta r sin \vartheta}{r^4 cos^4 \vartheta + r^2 sin^2 \vartheta} =

lim_{r \rightarrow 0} \frac{r^2 cos^4 \vartheta sin \vartheta}{r^2 cos^4 \vartheta + sin^2 \vartheta}[/tex]

I got that far, but I'm not sure how to get rid of the r^2 in the denominator.

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# 2 variable limit

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