# Study Guide - Chapter 13

## Math 221

- Sketch several level curves. Look at problems 1 - 4 in the chapter review.
- Discuss the continuity of the funciton and evaluate the limit, if it exists. Look at problems 7 -
10 in the chapter review.
- Find all first partial derivatives. Two parts. Look at problems 11 - 19 in the chapter review.
- 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.
- Find the directional derivative in the indicationd direction at the specified point. Look at
problems 39 - 42 in the chapter review.
- 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.
- 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.
- Locate and classify any extrema of the function. Look at problems 53 - 56 in the chapter
review.
- 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).

- 13.1.68
- 13.3.68
- 13.4.26
- 13.5.28
- 13.7.36
- 13.9.22
- 13.9.34
- 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.