# Study Guide - Chapter 12

## Math 221

1. Find the indicated limit. Look at problems 15 - 16 in the chapter review*.
2. For two vector valued functions, find the first and second derivatives of one, and the first derivative of the dot product and cross product of the pair. Look at problems 17 - 18 in the chapter review*.
3. Find the indefinite integrals. Two parts. Look at problems 21 - 24 in the chapter review*.
4. Find the velocity, speed and acceleration at time t. Then, find the tangential and normal components of acceleration and the curvature at time t. Formulas are provided for the tangential and normal components of acceleration and for the curvature. Look at problems 33 - 38 in the chapter review*.
5. Find the length of the space curve over the indicated interval. Look at problems 41 - 42 in the chapter review*.
*Problem are directly from the chapter review.

The in-class portion of the test is 75 points.

The take-home portion of the test is 25 points and is given below.

1. 3.28
2. 3.32
3. 3.44
4. 4.38 / 4.40
5. Review.30