the
solid
that
lies under
the
graph
of
f(x,
y)
and
above
the
region
~
equals
to
J
times
the
area
of
the
region;
~
J
=
5
and
there
is point
(x, y)
E
R
such
that
f(x,
y)
=
6,
there
is a point in
R
such
that
f(x,
y)
=
4;
(c)
If
Area(R)
=
5
and
2
<
f(x,
y)
::;
10,
then
f
fR
f(x,
y)dxdy
~
10.
(d)
If
fmin
and
fmax
are
the
minimal
and
the maximal values of
f
on a region
R,
then
fmin
.
Area(R)
::;
f
fR
f(x,
y)dA
:S
fmax
.
Area(R).
(3)
Which of
the
following is true:
,
(a)
f
JD
f(x,
y)
=
J~1
J~1
f(x,
y)dydx,
where
D
is
the
disk of radius 1 centered
at
!
~(O,O).
"'~:;7~r~"
(b)
a
lan:in~
lies entirely in
the
third
quadrant,
then
its
moment
M
x
with respect
'./
.
0
XaxIS
IS
negative,
(c)
Center
of mass of a
lamina
is a point which is on
the
lamina.
(d) Given
the
lamina's
mass m
and
moment
M
x
with respect
to
zaxis, you can find
its
moment
My
with
respect
to
yaxis.
(4) Which of
the
following represents
the
integral of
f(x,
y)
over
the
part
of
the
inside of
the
sphere
x
2
+
y2
+
z2
=
1
that
lies in
the
first
octant
(x,
y,
z
~
0):
z 2
~()
\r~
rV
1

_
y
2
f(
)d
d
~o
Jo
x,y,Z
xdy
Zj
2
0)
000
[
:1;£<,/1
(x
+1;2)
J(x,
u.
Z dxdydz;
)
'"
b
rl
r~
rV
1

y
2
(
)
()
c
Jo Jo
Jo
f x, y, z dzdydx;
{d)
[1
rVIXLy2
cv'f=X1
r(
,
)d
d d .
vO
:>i1
)0
J
$,~,
Z
11
z
x,