Page 1 of 4
MAC 2313
Name_________________________________
Test 3
Date: March 18, 2010
For full credit, clearly show all work that justifies your answer.
1.
(8 points) Set up,
but do not evaluate
, a double integral that represents the volume of
the solid in
R
3
bounded by the cylinder
1
2
2
=
+
y
x
and the planes
z
= 8 and
x
+
y
+
z
= 2.
Express your answer as an iterated integral.
2.
(8 points)
Set up,
but do not evaluate
, an expression that would give the
x
coordinate of the center of mass of the lamina that occupies the region bounded by
the graphs of
x
y
=
,
y
= 0, and
x
= 1, where the density function
xy
y
x
=
)
,
(
ρ
.
Express double integrals as iterated integral.
3.
(8 points) Find the directional derivative of
)
ln(
)
,
(
3
2
y
x
y
x
f
+
=
at
P
(2,1) in the
direction of
Q
(1,5).
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentPage 2 of 4
4.
(8 points) Determine the number of saddle points of
4
2
3
2
3
)
,
(
y
y
x
x
y
x
f
+
−
−
=
.
5.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Spring '08
 Paris
 Calculus, Derivative

Click to edit the document details