Go to Study Guide for Exam 1
Go to Study Guide for Final Exam


This exam will cover material from sections 13.1-13.10. Anything not covered in class or given for homework will not be on the exam. Also excluded:

• Continuity of composite functions, f(g(x,y))(13.2)
• Definition of Differentiability(13.4)
• Applications involving differentials(13.4)
• Implicit differentiation formulas(13.5)
• Normal lines(13.7)
• Two constraints with LaGrange multipliers(13.10)

The test material will be from the following categories:

1. Functions of Several Variables: domain(incl sketching), range, level curves/contour maps, simple level surfaces
2. Limits: finding a limit using the definition(ε-δ), definition of continuity, showing limit exists/doesn't exist
3. Partial Derivatives: limit definitions, geometric interpretation, calculating first or higher partial derivatives, tangent planes
4. Chain Rule: Variations, including writing out multilayer chain rules for general functions
5. Differentials: comparison to Δz, error analysis
6. Directional Derivatives: calculation, geometric interpretation
7. Gradients: calculation, interpretation and significance
8. Extreme Values: relative, absolute, saddle points, 2nd Partial Derivatives Test, Lagrange Multipliers, applications

The problems will be of a similar type to the homework and examples from lecture. There will not be any proofs on this exam. There will likely be at least one problem that requires you to either sketch a domain or contour map, or match up appropriate functions, graphs, and/or contour maps. Scientific or graphing calculators (similar to TI-83/84) are permitted, but ones that can do symbolic derivatives/integrals (e.g., TI-89) are not.

Last uploaded June 24, 2011