a) Determine the gradient of $f(x, y, x) = \ln(x^2 + y^2 + 2z^3)$ at $(3, 2, 1)$.
b) Consider the surface
$f(x, y, z) = \frac{3x^4}{\sqrt{y^3}} - z\sqrt{y^3} + 5x^2\sqrt{z} = 0$
for $x, y, \& z$ all $> 0$. Determine the component of a vector normal to this
surface at $(0, 1, 2)$ in the direction of the vector $\vec{A} = \hat{i} + 2\hat{k}$.
