# Math 221: Chapter 15 Exam Study Guide

## In-Class Exam

1. Determine whether the vector field is conservative. If it is, find the potential function. Three parts.
2. Find the divergence and curl for the vector field.
3. Evaluate the line integral ∫F·dr. Two parts.
4. Parameterize a piecewise smooth curve and then evaluate the line integral.
5. * Use Green's Theorem to evaluate the line integral.
6. Find a vector valued function r(u,v) for each of the indicated surfaces. Write them in rectangular form. Three parts.
7. Use the fundamental theorem of line integrals to evaluate the line integral. Three parts.
8. * Evaluate the surface integral.
9. * Find the flux through the surface.
10. * Use the divergence theorem to find the outward flux through the solid.
11. * Use Stoke's theorem to evaluate the line integral.

## Take Home Exam

1. Given a vector-valued function, find the partial derivatives, a normal vector, the parametric equations of the normal line, the equation of the tangent plane, and approximate the surface area.
2. Graph the solid described and use the divergence theorem to find the outward flux of the vector field through the solid.
3. Graph the surface described and then find the surface area..

## Notes

• For *'d problems (5, 8, 9, 10, and 11), set up the integral and change any variables necessary to perform the integration, but stop without performing the actual integration. For the other problems, you need to work out the integrals.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 TH1 TH2 TH3 Total 9 6 8 6 6 9 9 6 6 6 6 15 4 4 100