073894…: “Back to the gold icosahedron”

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Consider $F(x,y) = \frac {x^3 y - y^3 x}{x^4+y^4}$ . Let $C$ be the curve traced out by $\vec {p}(t) = \vector {2t,t}$ for $t> 0$ . Is $C$ part of a level curve of $F$ ?

Yes No

Which level curve is it? $F(x,y) = \answer {6/17}$

Compute the limit below, if it does not exist, write $\verb |DNE|$ . $\lim _{\vector {x,y}\to \vector {0,0}} F(x,y) = \answer {DNE}$

Is the following function continuous on $\R ^2$ ? $G(x,y) = \begin {cases} F(x,y) &\text {if $(x,y)\ne (0,0)$},\\ 0 &\text {if $(x,y) = (0,0)$}. \end {cases}$

Yes No