# Math 221: Chapter 14 Study Guide

1. Find the limit, if the limit exists. Three parts.
2. Find fx(x,y) and fy(x,y).
3. Find the differential.
4. Use Lagrange multipliers to find the maximum and minimum values of f subject to the given constraint. Also, find the points at which these extreme values occur.
5. Find the directional derivative of f at P in the direction of a.
6. Locate all relative maxima, relative minima, and saddle values, if any.
7. Find equations for the tangent plane and normal line to the given surface at the point P.
8. Use a total differential to approximate the change in the values of a function from point P to point Q.
9. Use the chain rule to find the partial derivatives and the derivative. Three parts.
10. Find the gradient of f at the indicated point. Find unit vectors in the directions in which f increases and decreases most rapidly at P; and find the rate of change of f at P in those directions.
11. Find parametric equations of the tangent line at the given point to the curve of intersection of two surfaces.
12. Find some second order partial derivatives. Three parts.
13. Identify the three dimensional surface (see chapter 12). Six parts.
14. Find the scalar tangential and normal components of acceleration at the given time.
15. Find an arc length parametrization of the function that has the same orientation and the indicated reference point.

## Notes

• Some of the problems may be directly from the text.
• The questions are worth a lot of points each since there aren't very many of them.

## Points per problem

 # Pts 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 Total 15 10 5 10 8 10 10 7 15 10 10 12 12 8 8 150