# Math 221: Chapter 12 Exam Study Guide

1. Given two points, find a vector-valued function for the segment between them. Also write a set of parametric equations for the line segment.
2. Represent the curve as a vector-valued function. Three parts.
3. Find the limits. Three 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 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.
7. Use the acceleration function and initial conditions to find the velocity and position functions.
8. Find a unit tangent vector at the indicated point.
9. Find the curvature and radius of curvature for an explicitly defined plane curve.
10. Find the tangential and normal components of acceleration.
11. 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.
12. Find the length of the space curve.
13. Application problem involving path of a projectile.
14. 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

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Total 6 9 9 12 6 10 5 5 6 8 6 4 6 8 100