# Math 221: Chapter 12 Exam Study Guide

- Given two points, find a vector-valued function for the segment between them. Also write a set of parametric equations for the line segment.
- Represent the curve as a vector-valued function. Three parts.
- Find the limits. Three 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 and acceleration both at an arbitrary time t and at a specific time. Then sketch the velocity and acceleration vectors on the graph and label them.
- Use the acceleration function and initial conditions to find the velocity and position functions.
- Find a unit tangent vector at the indicated point.
- Find the curvature and radius of curvature for an explicitly defined plane curve.
- Find the tangential and normal components of acceleration.
- Given a space curve, find the unit tangent vector and parametric equations for the tangent line at a particular point. Then find the principal unit normal vector to the curve at a point.
- 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 1-9 are to be worked without a computer.
- Questions 10-14 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.
- You may find the Introduction to Maxima for Multivariate Calculus or Maxima
Book to be useful.

## Points per problem

# |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
Total |

Pts |
6 |
9 |
9 |
12 |
6 |
10 |
5 |
5 |
6 |
8 |
6 |
4 |
6 |
8 |
100 |