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:

# 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