2. $f(x, y) = \frac{x^2}{\sqrt{xy}}$, $g(x, y) = \frac{x^2 - 9y^2}{4y^2 - 4x^2}$, $h(x, y) = \frac{y^2 - x^6}{x^3y}$
a. Find and sketch the domains of $f$, $g$ and $h$.
b. Find $\lim_{(x, y) \to (2, 1)} f(x, y)$, $\lim_{(x, y) \to (0, 11)} g(x, y)$, $\lim_{(x, y) \to (3, 3)} h(x, y)$.
c. Show that $\lim_{(x, y) \to (0, 0)} f(x, y)$, $\lim_{(x, y) \to (0, 0)} g(x, y)$, $\lim_{(x, y) \to (0, 0)} h(x, y)$ does not exist.
d. Find $\nabla f(x, y)$, $\nabla g(x, y)$, $\nabla h(x, y)$.