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MA
201
Studv Guide for
Test
2
You
need
to
know:
The graph
of
z
=
f
(x,y)
is a surface in 3space'
A fevel cLlrve
is a set of
points
where
f
(x,y)= some constant
k.
Must be able to approach
(a, b) from any direction, along any
path,
for
/(r,.v)
to
have a limit at (a, b), must have limit at (a, b) to be continuous at
(a, b)'
ARule
of
thumb: ii t is
given by a formula in elementary functions' then
f is
continuous
wherever it
is welldefined.
,
..The
Heart of Calculus Formula for functions
of multiple variables:
.{{I
+;g)
=./(i)
+ V.f
.;6
(Okay, so you don't have
to actually know this,
but it
sure looks nice.)
rlMaximum
rate of change of a function occurs in direction of the gradient'
.$The gradieni vecior is
perpendicular to level curves of the function.
:f
A continuous function on a closed,
pounded set attains an absolute
maximum
and absoluie minimum on that set
.
''
You
need
to
be able
to:
Find
partial derivatives

differentiate with respect to one variable while treating
the other(s) as constants.
Recognize and interpret both ways of writing
partial derivatives'
:.,.Use
ilairaut's
Theoiem {and
rernember to say that
you are using it and, if
necessary,
justifY its use)
Find the equation of
the
plane tangent to the graph
of z
=
f
(x,.:')
at
('tto'"1'o
)
'
,,.
.Oraw
a tree cliagram(if
you need it) and use the chain rule to find needed
partials'
Find the gradient
vector for a function.
Find the directional
derivative
of
/(t)
at
io
in the direction
of it
'
Find the maximum rate of change of a
function at a
point, and the direction in
which it occurs.
Find critical
points of a function of two variables'
Remember
and apply the second derivatives
test'
Find the absolute
maxirnum and absolute
minimum of a continuous
function on
a
closed, bounded set.
Evaluate an iterated integral, set up and evaluate a simple double integral'
Some SamPle Problems:
pp. 660_662
iO,t
115,1720,21,23a,24a,33,34,
36, 41
,42,43,
44,45,4749,
51)
'p.lzg(36,15,16,17iorsimilarproblemsinSection12'2)}
CaX"
tr:i:w./.t
*rr,
6..ii
.
4''$l'