- Find a function $f(x,y)$ so that $Df(x,y) = \begin{bmatrix}2x+3y&3x+4y\end{bmatrix}.$
- Find the work done by $\vec F = (3,4,-2)$ on an object that moves from $(0,2,1)$ to $(3,1,5)$. Does the path matter?
- Consider the function $f(x,y)=x^2+\frac{3y^2}{2}$
- Set up an integral for $\int_C f \, ds$ where $C$ is a circle of radius 3.
- Compute $\nabla f$ and then find the circulation and total flux of $\nabla f$ on the contour $C$.
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