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MATH 141B
QUIZ#5 Solutions
Date: Fri Feb 15, 2008
Instructor: Dr. M.Fabbri
1.
i)
False
.
V
(
r, h
) =
πr
2
h,
whose graph is not a cylinder. An equation involving
r, h
and
V
whose graph in 3space (with axes
r, h
and
V
) is a cylinder is
h
2
+
r
2
= 1
.
Note that for each
±xed
V
you get a circle. The potential confusion here is that the function
V
arose by taking
the volume of a cylinder, but the graph of the function
V
(
r, h
) is not a cylinder.
ii)
False
. Fixing
r
=
r
0
gives
V
= (
πr
0
2
)
h,
which is a straight line.
iii)
True
. Fixing
h
=
h
0
gives
V
= (
πh
0
)
r
2
h,
which is a parabola.
Therefore, D) is the answer.
2.
∂g
∂v
=
u
cos(
uv
)

3
e
3
v
and so,
∂g
∂v
(
π,
0) =
π

3
.
Therefore, C) is the answer.
3.
i)
True
.
x
·
w
t
is the biomass of the trout (follow the units), and
y
·
w
b
is the biomass of the
bluegill. Therefore
x
·
w
t
+
y
·
w
b
is the total biomass (of the trout and the bluegill).
ii)
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This note was uploaded on 03/30/2008 for the course MATH 141B taught by Professor Marcfabbri during the Spring '08 term at Pennsylvania State University, University Park.
 Spring '08
 MARCFABBRI
 Math, Logic

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