- Sketch the graph of the 2D vector valued function and show the direction of increasing t.
- Find the limit of the vector valued function.
- Find the derivative of the vector valued function.
- Find parametric equations of the line tangent to the graph of the vector valued function at the given point.
- Evaluate the integral.
- Calculate a derivative using the chain rule.
- Find the derivative of a dot product and a cross product using the product rules for dot and cross products. Do not find the dot or cross product and then take the derivative.
- A 2D curve is given. Draw the unit tangent and unit normal vectors.
- A 3D curve is given. Identify the T, N, and B vectors (they are drawn, you just need to identify which one is which).
- Find parametric equations for the curve using arc length s as parameter.
- Find the unit tangent vector T, the unit normal vector N, and the binormal vector B, for the given value of t.
- Find the curvature and radius of curvature for a vector-valued function at the indicated point.
- Find the scalar tangential and normal components of acceleration at the indicated time t.
- Convert the rectangular equation into cylindrical and spherical coordinates.
- Use the given information to find the position and velocity vectors of the particle. Look at problems 13.6.15-18.
- Find the curvature for 2D function.
- Find the equation of the plane
- Convert the cylindrical equation into rectangular coordinates.

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

- Several of the problems are directly from the text.
- There is a page at the end of the test with r, r', and r" as well as ||r||, ||r'||, and ||r"|| for questions 10-13. It is intended to help speed up the process. That page also contains the formulas for the curvature in 2 dimensions. It does not contain the formulas you will need for questions 10-13, just some of the values you'll need.
- 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.

# | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | Total |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Pts | 6 | 6 | 6 | 6 | 6 | 6 | 10 | 6 | 4 | 5 | 5 | 5 | 5 | 8 | 8 | 6 | 6 | 6 | 110 |