# Study Guide - Chapter 13

## Math 221

1. Sketch several level curves. Look at problems 1 - 4 in the chapter review.
2. Discuss the continuity of the funciton and evaluate the limit, if it exists. Look at problems 7 - 10 in the chapter review.
3. Find all first partial derivatives. Two parts. Look at problems 11 - 19 in the chapter review.
4. Error analysis. Look at problems 33 - 36 in the chapter review. Be aware of the error that occurs when measuring. For example, if the ruler measures to the nearest 1/16th inch, then the error is +/- 1/32 inch.
5. Find the directional derivative in the indicationd direction at the specified point. Look at problems 39 - 42 in the chapter review.
6. Find the gradient and the maximum value of the directional derivative of the function at the specified point. Look at problems 43 - 46 in the chapter review.
7. Find the required derivatives using either the chain rule or substitution before differentiation. Look at problems 37 - 38 in the chapter review. The instructions in the review are to work the problem both ways, you are free to chose which way you want to work it on the exam.
8. Locate and classify any extrema of the function. Look at problems 53 - 56 in the chapter review.
9. Locate and classify any extrema of the function by using Lagrange multipliers.

The in-class portion of the exam is 60 points (6 points per problem). The take-home portion of the exam is worth 40 points (5 points each).

1. 13.1.68
2. 13.3.68
3. 13.4.26
4. 13.5.28
5. 13.7.36
6. 13.9.22
7. 13.9.34
8. Find the dimensions of right circular cylinder with volume 355 ml which minimizes the surface area (note: Surface Area, not Lateral Surface Area). Look at problem 13.10.32, but let v0=355 ml. I have set the problem up to find the cheapest Pepsi can.