## Math 221 - Chapter 14 Study Guide

1. Sketch the graph of the vector valued function and show the direction of increasing t. Look at problems 14.1.25-34*.
2. Find the limit of the vector valued function. Look at problems 14.2.13-18.
3. Find the derivative of the vector valued function. Look at problems 14.2.3-6*.
4. Find parametric equations of the line tangent to the graph of the vector valued function at the given point. Look at problems 14.2.23-26*.
5. Evaluate the integral. Look at problems 14.2.37-41*.
6. Find the derivative of a dot product using the product rule for dot products. Look at problem 14.2.55-56.
7. Find the derivative of a cross product using the product rule for cross products.
8. Determine whether r is a smooth function of the parameter t. Look at problems 14.3.3-6*.
9. Calculate a derivative using the chain rule. Look at problems 14.3.15-18*.
10. Find the arc length of the curve. Look at problems 14.3.7-14*.
11. 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 14.3.23-28*.
12. Find the unit tangent vector T and the unit normal vector N for the given value of t. Look at problems 14.4.3-10.
13. Find the binormal vector B=TxN. Look at problems 14.4.15-18*.
14. Find the curvature at the indicated point. Look at problems 14.5.11-14*.
15. Sketch the curve, calculate the radius of curvature at the indicated point, and sketch the osculating circle. Look at problems 14.5.31.
16. 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 14.6.1-4*.
17. Use the given information to find the position and velocity vectors of the particle. Look at problems 14.6.15-18*.
18. Find the displacement and the distance traveled over the indicated time interval. Look at problems 14.6.25-28.
19. Find the scalar tangential and normal components of acceleration at the indicated time t. Look at problems 14.6.31-38*.

Take Home Portion

1. Geosynchronous orbit. You will need to do some research to answer this question.
1. Find the altitude in miles of a communications satellite that is in geosynchronous orbit about the moon. Look at problems 14.7.6-8. (5 points)
2. Find the speed in miles per hour of a satellite that is in geosynchronous orbit about the moon. Look at problem 14.7.7. (5 points)
2. Work problem 14.6.71. Show work (except for part b and then show what you're integrating). (5 points)

### Notes:

• Ģ*'d problems are directly from the text.
 # 1 2 3 4 5 6 7 8 9 10 Pts 4 4 4 4 4 5 5 4 4 4 # 11 12 13 14 15 16 17 18 19 Total Pts 4 5 5 4 5 5 5 5 5 85