# Math 221: Chapter 12 Exam Study Guide

- Given two points, find a vector-valued function for the segment between them.
- Represent the curve as a vector-valued function. Two parts.
- Find the limits. Two parts.
- Given two vectors, find their derivatives, the derivative of the dot product, and the derivative of the cross product.
- Find the indicated integral. Two parts.
- Given a two dimensional position function, find the velocity, acceleration, and speed at a specific time. Then sketch the velocity, acceleration, unit tangent, and unit normal vectors on the graph and label them.
- Find the curvature and radius of curvature for an explicitly defined plane curve.
- Find the tangential and normal components of acceleration.
- Find the length of the space curve.
- Application problem involving path of a projectile.
- Find the unit tangent, normal, and binormal vectors at the indicated point. Also find the curvature at the same point.

## Notes

- Questions 1-7 are to be worked without a computer.
- Questions 8-11 are to be worked using Maxima.
- You may copy the formulas from the summary table on page 877 onto a sheet of paper and use those during the exam. In addition to the formulas presented on that page, include
**B**=(**r**'×**r**")/||**r**'×**r**"|| and **N**=**B**×**T**.
- You may find the Introduction to Maxima for Multivariate Calculus or Maxima
Book to be useful.
- The Graphics
with Maxima book provides some really useful information as well.

## Points per problem

# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
Total |

Pts |
5 |
10 |
10 |
15 |
10 |
10 |
10 |
5 |
5 |
10 |
10 |
100 |