1) Find the gradient and Laplacian of this function: $xy(x^2+y^2-5z^2)$
2) Consider the following force: \(\vec{F} = y\hat{i} + x\hat{j} + \hat{k}\)
a) Is this force conservative? Give proof.
b) Calculate the work done by the force along a straight line $y = x$ from $(x,y) = (0,0)$ to $(x,y) = (1,1)$
c) Calculate the work done by the force along a parabola $y = x^2$ from $(x,y) = (0,0)$ to $(x,y) = (1,1)$
3) Use Green's Theorem to evaluate the closed path integral: $\oint (2y \,dx - 3x \,dy)$ around a
square bounded by $x = 3$, $x = 5$ and $y = 1$, $y = 3$.
