8df6f6…: “Right of the winter icosahedron”

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Let $F(x,y)=e^{-(x^2+y^2)}\sin (x^2+y^2)$ . Determine the equations and shapes of the cross-sections when $x=0$ , $y=0$ , $x=y$ , and describe the level curves.

$\text {When $x=0$, the cross-sections are given by } z=\answer {e^{-y^2}\sin (y^2)}$ $\text {When $y=0$, the cross-sections are given by } z=\answer {e^{-x^2}\sin (x^2)}$ $\text {When $x=y$, the cross-sections are given by } z=e^{\answer {-2}x^2}\sin (\answer {2}x^2)$

The level curves are best described as:

diamonds squares circles lines of slope $1$ hyperbolas