A worker leaves home at 9:00 AM, travels 40 km to the office, and then returns home at 5:00 PM. What is the magnitude of the wor
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Observe that the given vector field is a gradient field:
Let , so that
Integrating the first equation with respect to , we get
Differentiating this with respect to gives
Now differentiating with respect to
gives
Putting everything together, we find a scalar potential function whose gradient is ,
It follows that the curl of is 0 (i.e. the zero vector).