(12 points) Partial credit problem. You must upload a scan of your solution at the end of the exam. Please show all of your workings for full points. Let S be the surface given by the portion of the graph of  that lies above the 1/8th of the unit disk in the -plane which is illustrated below. Compute

Which integral computes the volume of the solid bounded by

Find the osculating plane to the curve , parametrized by

Compute the work done by the vector field in moving a particle along a curve which begins at and ends at.

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(12 points) Partial credit problem. You must upload a scan of your solution at the end of the exam. Please show all of your workings for full points. Let

The picture below illustrates level sets of which function:

Which of the following integrals computes the distance traveled by a particle moving with position vector

Consider a particle, which starts at the point , and travels one full revolution, counter-clockwise, around the unit circle. Use Green’s theorem to find the work done by the vector field

What hormone stimulates sperm production?