# Math 221: Chapter 13 Study Guide

1. Sketch the graph of the vector valued function and show the direction of increasing t. Look at problems 13.1.25-34.
2. Find the limit of the vector valued function. Look at problems 13.2.1-6.
3. Find the derivative of the vector valued function. Look at problems 13.2.11-14.
4. Find parametric equations of the line tangent to the graph of the vector valued function at the given point. Look at problems 13.2.23-26.
5. Evaluate the integral. Look at problems 13.2.35-46.
6. Find the derivative of a dot product using the product rule for dot products. Look at problems 13.2.33-34.
7. Find the derivative of a cross product using the product rule for cross products. Look at problems 13.2.33-34.
8. Calculate a derivative using the chain rule. Look at problems 13.3.15-18.
9. Find the arc length of the curve. Look at problems 13.3.7-14.
10. Find parametric equations for the curve using arc length s as parameter. Use the point on the curve where t=0 as reference. Look at problems 13.3.23-28.
11. Find the unit tangent vector T, the unit normal vector N, and the binormal vector B, for the given value of t. Look at problems 13.4.15-19.
12. Find the curvature for a vector-valued function at the indicated point. Look at problems 13.5.3-14.
13. Find the curvature and radius of curvature for the parametrically defined curve at the indicated point, and sketch the osculating circle. Look at problems 13.5.25-30.
14. Given the position vector of a particle moving in the plane. Find the velocity, acceleration, and speed at an arbitrary time t; then sketch the path of the particle together with the velocity and acceleration vectors at the indicated time t. Look at problems 13.6.1-4.
15. Use the given information to find the position and velocity vectors of the particle. Look at problems 13.6.15-18.
16. Find the displacement and the distance traveled over the indicated time interval. Look at problems 13.6.25-28.
17. Find the scalar tangential and normal components of acceleration at the indicated time t. Look at problems 13.6.31-38.

## Take Home Portion

1. Find the altitude in miles of a communications satellite that is in geosynchronous orbit about the moon. Look at example 1 in section 13.7 and problems 13.7.6-8. (5 points)
2. Find the speed in miles per hour of a satellite that is in geosynchronous orbit about the moon. Look at problem 13.7.7. (5 points)
3. Work problem 13.6.71. Show work (except for part b and then show what you're integrating). (5 points)

## Notes:

• Many of the problems are directly from the text.
• There is a take home portion of the exam worth 15 points. It is due the day after the exam.
• You will need to do some research to answer questions 1 and 2 on the take home exam.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 Total 5 4 4 5 5 4 4 4 5 6 8 4 5 6 5 6 5 85