Math 280
Fall 2009
Exam 3 Review
Disclaimer: I have attempted to be comprehensive in the
following, but important items may have been omitted by mistake. If
you see such an omission, please let me know, but you are responsible
for all of the lecture material to date.
The third hour exam for Math 280 will be held on Friday, November 13, and
will cover section 12.2 through section 13.1 (skipping sections 12.8 and
12.9) of the textbook. In particular, be prepared
to:
- Be able to compute limits of functions of several variables and to show
why some limits do not exist.
- Be able to define continuity and to state the extreme value theorem for
continuous functions.
- Be able to define partial derivatives and to compute partial derivatives
from the definition.
- Be able to compute partial derivatives, second partials directly and
through the chain rule.
- Be able to compute gradients and directional derivatives. Know the
properties of the gradient.
- Be able to compute tangent planes and use tangent planes for
approximations. Be able to compute upper bounds for error in linear
approximations.
- Be able to use first and second partials to find local extrema of a
function and decide whether they are local maxima, minima, or saddle points.
- Be able to integrate functions of two variables over rectangular
regions.
Any questions? Please ask!