Studv Guide for
is a surface in 3-space'
A fevel cLlrve
is a set of
(x,y)= some constant
Must be able to approach
(a, b) from any direction, along any
have a limit at (a, b), must have limit at (a, b) to be continuous at
thumb: ii t is
given by a formula in elementary functions' then
Heart of Calculus Formula for functions
of multiple variables:
(Okay, so you don't have
to actually know this,
sure looks nice.)
rate of change of a function occurs in direction of the gradient'
.$The gradieni vecior is
perpendicular to level curves of the function.
A continuous function on a closed,
pounded set attains an absolute
and absoluie minimum on that set-
differentiate with respect to one variable while treating
the other(s) as constants.
Recognize and interpret both ways of writing
rernember to say that
you are using it and, if
justifY its use)
Find the equation of
plane tangent to the graph
a tree cliagram(if
you need it) and use the chain rule to find needed
Find the gradient
vector for a function.
Find the directional
in the direction
Find the maximum rate of change of a
function at a
point, and the direction in
which it occurs.
points of a function of two variables'
and apply the second derivatives
Find the absolute
maxirnum and absolute
minimum of a continuous
closed, bounded set.
Evaluate an iterated integral, set up and evaluate a simple double integral'
Some SamPle Problems: