# Math 221: Chapter 15 Exam Study Guide

## In-Class Exam

- Evaluate the line integral. Be sure to check to see if the vector field is conservative and independent path. Three parts.
- Find a vector valued function
**r**(u,v) for each of the indicated surfaces. Write them in rectangular form. Three parts.
- Evaluate the surface integral.
- Parameterize a piecewise smooth curve and then evaluate the line integral.
- Use Green's Theorem to evaluate the line integral.
- Find the flux through the surface.
- Use the divergence theorem to find the outward flux through the solid.
- Use Stoke's theorem to evaluate the line integral.
- Given a parametric surface, find
**r**_{u} and **r**_{v}. Then find a vector **N** that is normal to the surface. Find parametric equations of the normal line at the indicated point. Find the equation of the tangent plane at the indicated point, and approximate area of the surface at the indicated point.

## Notes

- You may use Maxima, winplot, or dpGraph for the entire exam.

## Points per problem

# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
Total |

Pts |
24 |
18 |
6 |
6 |
6 |
6 |
6 |
6 |
22 |
100 |