Download Calculus 3 Exam 3 Practice and more Exams Calculus in PDF only on Docsity!
Department of Mathematics
MAC 2313
Exam 3A
Spring 2018
A. Sign your bubble sheet on the back at the bottom in ink.
B. In pencil, write and encode in the spaces indicated:
Name (last name, first initial, middle initial)
UF ID number
Section number
C. Under “special codes” code in the test ID numbers 3, 1.
1 2 • 4 5 6 7 8 9 0
D. At the top right of your answer sheet, for “Test Form Code”, encode A.
E. 1) This test consists of 15 multiple choice questions worth 69 points and 2 free response
questions worth 20 points. The test is counted out of 80 points, and there are 9 bonus points available.
The time allowed is 90 minutes.
You may write on the test.
Raise your hand if you need more scratch paper or if you have a problem with your test. DO NOT LEAVE YOUR SEAT UNLESS YOU ARE FINISHED WITH THE TEST.
F. KEEP YOUR BUBBLE SHEET COVERED AT ALL TIMES.
G. When you are finished:
Before turning in your test check carefully for transcribing errors. Any mis- takes you leave in are there to stay.
You must turn in your scantron and tearo↵ sheets to your discussion leader or exam proctor. Be prepared to show your picture I.D. with a legible signature.
The answers will be posted in Canvas within one day after the exam. Your dis- cussion leader will return your tearo↵ sheet with your exam score in discussion. Your score will also be posted in Canvas within one week of the exam.
MAC 2313 Exam 3 1A
NOTE: Be sure to bubble the answers to questions 1 15 on your scantron.
Questions 1 12 are worth 5 points each.
- Evaluate
Z Z
R
x sin(xy) dA, where R is the rectangle [1, 2] ⇥ [0, ⇡].
a.
b. 1 c. 2 d.
e. 1
- If f (x, y) is continuous, then
Z 2
1
Z (^) ln x
0
f (x, y) dy dx =
a.
Z 2
0
Z 2
ey
f (x, y) dx dy
b.
Z 2
1
Z (^) ex
2
f (x, y) dx dy
c.
Z (^) ln(2)
0
Z 2
ey
f (x, y) dx dy
d.
Z 1
ln(2)
Z (^) ex
2
f (x, y) dx dy
e.
Z (^) ln(2)
0
Z (^) ey
0
f (x, y) dx dy
- Identify the surface ⇢ = 2 csc .
a. The plane z = 2
b. The cone z =
p 2 x^2 + 2y^2
c. The cylinder x 2
d. The sphere x 2
e. The sphere x^2 + y^2 + z^2 = 4
5 cos^ xy^5 cos^ Tx^ x
0
(^2 1 )
0
p Fix
0
esing
MAC 2313 Exam 3 3A
- Let E be the solid bounded between z =
p x^2 + y^2 and z =
p 3 x^2 + 3y^2 within the
sphere x^2 + y^2 + z^2 = 4. Then
Z Z Z
E
z dV =
a.
Z 2 ⇡
0
Z ⇡/ 3
⇡/ 4
Z 2
0
3 sin 2 d⇢ d d✓
b.
Z 2 ⇡
0
Z ⇡
⇡/ 3
Z 2
0
3 sin 2 d⇢ d d✓
c.
Z 2 ⇡
0
Z ⇡/ 4
⇡/ 6
Z 2
0
⇢ cos d⇢ d d✓
d.
Z 2 ⇡
0
Z ⇡
⇡/ 4
Z 2
0
3 sin cos d⇢ d d✓
e.
Z 2 ⇡
0
Z ⇡/ 4
⇡/ 6
Z 2
0
3 sin cos d⇢ d d✓
- Convert the point (1, 1 ,
p
- from rectangular to spherical coordinates (⇢, ✓, ).
a.
b.
c.
d.
e.
- Find the volume of the solid bounded by paraboloids z = 6 x 2 y 2 and z = 2x 2 + 2y 2 .
a. 2 ⇡ b. 3 ⇡ c. 4 ⇡ d. 6 ⇡ e. 8 ⇡
a seciny
tart
tan
0
4
0
P
the
in
tan (^0 1 ) (^3 )
O
F p^1050
E
cos
tan 0 1 0 3,
38 6
(^11 )
0
7r
2 1 21 6 r
ar
1
0 v^ B
Gr 3r^
I 7T
3r 3111 6 3 3 6T
4A MAC 2313 Exam 3
- Rewrite
Z 16
0
Z 4
p x
Z (^4) y
0
dz dy dx as an equivalent iterated integral in the order dy dx dz.
a.
Z 16
0
Z (^) (4 z) 2
0
Z (^4) z
p x
dy dx dz
b.
Z 4
0
Z (^) (4 z) 2
0
Z (^4) z
p x
dy dx dz
c.
Z 16
0
Z (^4) pz
0
Z (^4) z
0
dy dx dz
d.
Z 4
0
Z (^4) pz
0
Z (^4) z
0
dy dx dz
e.
Z 4
0
Z (^4) z
0
Z px
0
dy dx dz
- Which of the following represents the area of the region that lies inside r =
p 3 sin ✓ and outside r = cos ✓?
a.
Z ⇡
⇡/ 6
Z p3 sin ✓
cos ✓
r dr d✓
b.
Z ⇡
⇡/ 3
Z p3 sin ✓
cos ✓
r dr d✓
c.
Z ⇡
⇡/ 3
Z p3 sin ✓
0
r dr d✓ +
Z ⇡/ 2
⇡/ 3
Z (^) cos ✓
0
r dr d✓
d.
Z ⇡
⇡/ 3
Z p3 sin ✓
0
r dr d✓
Z ⇡/ 2
⇡/ 3
Z (^) cos ✓
0
r dr d✓
e.
Z ⇡
⇡/ 6
Z p3 sin ✓
0
r dr d✓
Z ⇡/ 2
⇡/ 6
Z (^) cos ✓
0
r dr d✓
9 4
z
y
Fx 4 2
y y
0
16
2
1
r (^) Bsint
men i c
Ly E
qn.lt
Eint
EEEsino
O
int
6A MAC 2313 Exam 3
- If R is the region within the ellipse
x^2
4
+y^2 = 1 and above x-axis, find the corresponding
region S in the uv-plane.
x
y
2
1
R
a.
u
v
1
⇡
S
b.
u
v
1
⇡
S
c.
u
v
1
S
d.
u
v
2
S
- Use the transformation to set up an integral over the region S for
Z Z
R
r x^2
4
a.
Z ⇡
0
Z 1
1
u du dv
b.
Z ⇡
0
Z 1
1
2 u 2 du dv
c.
Z ⇡
0
Z 1
0
2 u 2 du dv
d.
Z ⇡
0
Z 1
0
u 2 du dv
u 74
v (^) y y v
u tu
go
it
Enos
i'Eii.ie
i
man
É
Jix.gs (^) k 2
1
55
2 dad
81
v2 (^) r
0
AT
Si2r aviv
r
MAC 2313 Exam 3A, Part II Free Response
Name: Section #:
SHOW ALL WORK TO RECEIVE FULL CREDIT
- (10 points)
(a) Let D be the triangle in the xy-plane with vertices ( 1 , 2), (1, 0), and (1, 4). Write the
integral
Z Z
D
xy dA as one iterated integral.
Hint: Determine the order of integration dxdy or dydx first.
D
Z Z
D
xy dA =
Z Z
xy
(b) Evaluate the integral
Z p 2
0
Z p 4 x 2
x
p 1 + x^2 + y^2
dy dx.
y x^
(^3) I (^) Y L 3
X 1
g xt
y
Iii
dydx 1
y x
Fiji of
Sif
drao
SIT (^2) Fr lido
SEErs (^) I do OCT^1 É
F 1 F 1
