- Sketch the graph of the vector valued function and show the direction of increasing t. Look at problems 14.1.25-34*.
- 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 14.2.55-56.
- 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 problems 14.4.3-10. - Find the binormal vector
**B**=**T**x**N**. 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 14.6.15-18*.
- Find the displacement and the distance traveled over the indicated time interval. Look at problems 14.6.25-28.
- Find the scalar tangential and normal components of acceleration at the indicated time t. Look at problems 14.6.31-38*.

**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 points)

- •*'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 |