Math 221 - Chapter 14 Study Guide
- Sketch the graph of the vector valued function and show the direction of increasing t. Look at
- Find the limit of the vector valued function. Look at problems 14.2.13-18.
- Find the derivative of the vector valued function. Look at problems 14.2.3-6*.
- 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*.
- Evaluate the integral. Look at problems 14.2.37-41*.
- Find the derivative of a dot product using the product rule for dot products. Look at problem
- Find the derivative of a cross product using the product rule for cross products.
- Determine whether r is a smooth function of the parameter t. Look at problems 14.3.3-6*.
- Calculate a derivative using the chain rule. Look at problems 14.3.15-18*.
- Find the arc length of the curve. Look at problems 14.3.7-14*.
- 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*.
- Find the unit tangent vector T and the unit normal vector N for the given value of t. Look at
- Find the binormal vector B=TxN. Look at problems 14.4.15-18*.
- Find the curvature at the indicated point. Look at problems 14.5.11-14*.
- Sketch the curve, calculate the radius of curvature at the indicated point, and sketch the osculating
circle. Look at problems 14.5.31.
- 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*.
- Use the given information to find the position and velocity vectors of the particle. Look at problems
- Find the displacement and the distance traveled over the indicated time interval. Look at problems
- Find the scalar tangential and normal components of acceleration at the indicated time t. Look at
Take Home Portion
- Geosynchronous orbit. You will need to do some research to answer this question.
- 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)
- 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)
- Work problem 14.6.71. Show work (except for part b and then show what you're integrating). (5
- •*'d problems are directly from the text.