- Consider a wire that lies along the ellipse $x^2/4+y^2/9=1$. Set up an integral that gives the mass of this wire if the density (mass/length) is $\delta(x,y) = x^2+y^2$.
- Find a function $f(x,y)$ so that $\nabla f = (y^2,2xy+10)$. Then compute $D^2f$.
- Find a potential for $\vec F = (2x+3yz,3xz+y,3z)$, or expain why none exists.
- Find a potential for $\vec F = (2x+3yz,3xz+y,3xy)$, or expain why none exists.
- Find the work done by the vector field in #2 to move an object from the point $(2,3)$ to the point $(-1,4)$.
- Find the work done by the vector field in #4 to move an object from the point $(1,2,3)$ to the point $(-1,4,0)$.
- Find the work done by the vector field in #4 to move an object along any path that starts at $(a,b,c)$ and ends at $(a,b,c)$.
- Find a potential for $\vec F = \dfrac{(-x,-y,-z)}{(x^2+y^2+z^2)^{3/2}}$.
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