MAT 267
TEST 2
REVIEW
NOTE:
Below the Examples and hw refer to examples and homework from the textbook,
ww
refers to webwork hw
problems.
CHAPTER 11
11.1
Know how to:
•
Sketch the graph of basic surfaces
(Examples 3,4, hw 18).
•
Find the domain of two and three variable functions (Examples 1,2,10, ww 1, 2, hw 4, 8 ).
•
Know how to graph level curves (Examples 6, 7, 8, 9, ww 6) and be able to match graphs of 3 dimensional surfaces and
their contour maps (ww 4,5, hw
21, 22).
•
Know how to find equations for the level surfaces of a three variable function (Example 11) .
11.3
Know how to
•
Find partial derivatives of two and three variable functions algebraically (Examples 1, 3,5, ww 1-8),
and how to
estimate their value given the contour plot of the function
(hw 2). Understand the geometrical meaning of the partial
derivative with respect to
x
(rate of change in the direction of the positive
x
-axis) and
y
(rate of change in the direction of
the positive
y
-axis) (Example 2, hw 2,3,4).
•
Find higher order partial derivatives (Examples 6 and 7, ww 7, 8).
•
Differentiate implicitly if
z
is defined implicitly as a function of
x
and
y
(Example 4, ww 9). (Note that in section 11.5 a
very convenient formula for implicit differentiation is derived).
11.4
Be able to
•
Find the equation of the tangent plane
to a surface
z
=
f
(
x
,
y
) at a given point
P
0
=
x
0
, y
0
, z
0
:
z
=
z
0
f
x
x
0
, y
0
x
−
x
0
f
y
x
0
, y
0
y
−
y
0
(Example 1, ww 1, 2)
•
Find linear approximation
(local linearization) of a two variable function
f
(
x
,
y
) at a given point
x
0,
y
0
:
L
x , y
=
f
x
0,