# Math 221: Chapter 12 Exam Study Guide

1. Given two points, find a vector-valued function for the segment between them.
2. Represent the curve as a vector-valued function. Two parts.
3. Find the limits. Two parts.
4. Given two vectors, find their derivatives, the derivative of the dot product, and the derivative of the cross product.
5. Find the indicated integral. Two parts.
6. 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.
7. Find the curvature and radius of curvature for an explicitly defined plane curve.
8. Find the tangential and normal components of acceleration.
9. Find the length of the space curve.
10. Application problem involving path of a projectile.
11. 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=(rr")/||rr"|| 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

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