SEAN CHEN
Math5CA1M10Wirts
WeBWorK assignment number 5B
Review is due : 07/01/2010 at 05:00am PDT.
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some kind of mistake. Usually you can attempt a problem as many times as you want before the due date. However, if you are
having trouble figuring out your error, you should consult the book, or ask a fellow student, one of the TA’s or your professor for
help. Don’t spend a lot of time guessing – it’s not very efficient or effective.
Give 4 or 5 significant digits for (floating point) numerical answers.
For most problems when entering numerical answers,
you can if you wish enter elementary expressions such as 2
∧
3 instead of 8,
sin
(
3
*
pi
/
2
)
instead of 1,
e
∧
(
ln
(
2
))
instead of 2,
(
2
+
tan
(
3
))
*
(
4

sin
(
5
))
∧
6

7
/
8 instead of 27620.3413, etc. Here’s the
list of the functions
which WeBWorK understands.
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1.
(1 pt)
By changing to polar coordinates, evaluate the integral
ZZ
D
(
x
2
+
y
2
)
11
/
2
dxdy
where
D
is the disk
x
2
+
y
2
≤
16.
The value is
.
2.
(1 pt) Using geometry, calculate the volume of the solid
under
z
=
4

x
2

y
2
and over the circular disk
x
2
+
y
2
≤
4.
3.
(1 pt)
Using polar coordinates, evaluate the integral
ZZ
R
sin
(
x
2
+
y
2
)
dA
where R is the region 16
≤
x
2
+
y
2
≤
36.
4.
(1 pt)
Find
ZZ
R
f
(
x
,
y
)
dA
where
f
(
x
,
y
) =
x
and
R
= [
1
,
2
]
×
[
2
,
5
]
.
ZZ
R
f
(
x
,
y
)
dA
=
5.
(1 pt) Evaluate the double integral
I
=
ZZ
D
xydA
where
D
is the triangular region with vertices
(
0
,
0
)
,
(
4
,
0
)
,
(
0
,
3
)
.
6.
(1 pt) Match the following integrals with the verbal de
scriptions of the solids whose volumes they give. Put the letter
of the verbal description to the left of the corresponding integral.
1.
Z
2

2
Z
4
+
√
4

x
2
4
4
x
+
3
ydydx
2.
Z
1
√
3
0
Z
1
2
√
1

3
y
2
0
1

4
x
2

3
y
2
dxdy
3.
Z
1
0
Z
√
y
y
2
4
x
2
+
3
y
2
dxdy
4.
Z
1

1
Z
√
1

x
2

√
1

x
2
1

x
2

y
2
dydx
5.
Z
2
0
Z
2

2
4

y
2
dydx
A. Solid under an elliptic paraboloid and over a planar re
gion bounded by two parabolas.
B. Solid bounded by a circular paraboloid and a plane.
C. One eighth of an ellipsoid.
D. One half of a cylindrical rod.
E. Solid under a plane and over one half of a circular disk.
7.
(1 pt) Find
lim
(
x
,
y
)
→
(
0
,
0
)
x
3
y

xy
3

8
x
3

xy
or type ’N’ if the limit does not exist.
Consider the function
8.
(1 pt) Find
lim
(
x
,
y
)
→
(
0
,
0
)
6

y

e

x
2

y
2
cos
x
or type ’N’ if the limit does not exist.
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 Summer '06
 Roche
 Math, Derivative, Vector Calculus, Gradient

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