Show that the equation $2x^3+6xy^2+3x^2+3y^2-y=0$ defines a function $y=f(x)$ in the neighbourhood of $(0,0)$. Determine $\dfrac{f(x)}{x}$ and $\dfrac{f(x)}{x^2}$ as $x\to0$. Any leads?
2026-03-27 04:22:01.1774585321
Equation $2x^3+6xy^2+3x^2+3y^2-y=0$ defines $y$ as a function of $x$ around the origin
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