MATH 10B: Midterm - Sample
Solutions
(1) Evaluate
Z
0
1
Z
2
x + 2y dxdy .
0
Solution:
Z
0
1
Z
2
Z
x + 2y dxdy =
0
0
1
0
Z
=
x2
+ 2xy
2
x=2
x=0
dy
2 + 4y dy
1
= 2y + 2y 2
0
1
= 0
(2) Evaluate
Z
p
2
0
Z
p
sin(x2 ) dxdy
y/2
by changing the order of integrat
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Discussion Day/Time/TA:
Math 10B Winter 2014
Final Exam [for students in 1:10pm-2pm course]
March 18, 2014 (8am-11am)
You have 180 minutes to do this exam.
Turn o and put away your cell phones and earbuds.
You may not use calculators, bo
1. (10 points)
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r = 2 311166)
Compute the total shaded area.
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ROUND YOUR SECTION: 1013021 OR 10B022
Math 10B - Fall 2014
Practice Midterm exam Tuesday November 4, 2014
Instructions:
You have 50 minutes to do this exam.
Turn off and put away your cell phones and earbuds.
You may not use cal
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Math 10B - Fall 2014
Final exam - Saturday December 13, 2014
Instructions:
You have 180 minutes to do this exam.
Turn o and put away your cell phones and earbuds.
You may not use calculators, books or other assistance during the exa
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Math 10B - Spring 2015
Second Quiz - Wednesday May 13, 2015
1) Find the work done by the force eld F(x, y) = y 2 i + xyj on a particle that moves along
the curve y = 2x2 from (1, 2) to (1, 2).
2) Use Greens theorem to evaluate the l
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Math 10B - Spring 2015
First Quiz Wednesday April 15, 2015
Mum,
LlSet uggthe iterated integral that calculates ffR $y2 dA Where R is the region bounded by
:1: + y = 2 and 93 = 3/2 2y. Include a sketch of R. 2. Evaluate the fol
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Math 10B - Spring 2015
Second Quiz Wédnesday May 13, 2015
1) Find the work done by the force eld F(:z:7 y) 2 (1121 + xyj on a particle that moves along
the curve y = 2:132fr0m (1,2) to (132).
f wig 7% I,
Wait, :2 P v A5: \ IX 3&
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First Name:
Math 10B - Spring 2015
First Quiz - Wednesday April 15, 2015
1. Set up the iterated integral that calculates R xy 2 dA where R is the region bounded by
x + y = 2 and x = y 2 2y. Include a sketch of R.
2. Evaluate the following integ
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Math 10B - Spring 2015
Third Quiz - Wednesday May 27, 2015
1) (4 points) Calculate the vector line integral C Fds, where F(x, y) = (yexy , xexy + 2y)
and C is the oriented curve that starts at (0, 2) and ends at (3, 0). Note that C
MATH 10B: Final - Sample
Answers
(1)
Z
2
0
(2)
Z
0
Z
0
1Z 1
p
4Z
25 r2
r dz dr d = =
3
52
3
yey + yey + ey dy dx = = e
1
0
x3 y 2 z,
(3) F = rf where f =
so
Z
p
F ds = f ( 1, , 2)
f (1, 0, 0) =
2 2
x
(4)
X=
At (3, 1, 3):
Ts = (1, 0, 1),
(5)
9
s, t, 2
st
T
MATH 10B: Final - Sample
Some identities and formulas:
cos(2x) = 2 cos2 x
@(x, y)
= r,
@(r, )
1=1
@(x, y, z)
= r,
@(r, , z)
2 sin2 x
@(x, y, z)
= 2 sin '
@(, ', )
Do all 8 problems. No calculators are allowed. Simplify your answers as far as possible.
(1)
Math 10B - Calculus of Several Variables II
Quiz 2
April 22, 2011
Name:
Total
/10
Evaluate the integral:
3
2
2 sin ddd.
0
0
1
Extra credit: Thinking of this as an integral in spherical coordinates, what is the region it gives the volume of ? (The
extra cr
Math 10B - Calculus of Several Variables II
Quiz 1
April 8, 2011
Name:
Evaluate the following integral:
Z
2
0
Solution. First, since we cannot do the integral
at the region of integration:
y
R
e
Z
1
e
x2
dxdy:
y
2
x2
dx, we need to change the order of int
Math 10B - Calculus of Several Variables II - Winter 2011
March 9, 2011
Practice Final
Name:
There is no need to use calculators on this exam. All electronic devices should be turned o and put away.
The only things you are allowed to have are: a writing u
Math 10B - Calculus of Several Variables II
Quiz 5 Make Up
Due June 3, 2011
Name:
Instructions: This will allow you to make up points for quiz 5, raising your score to at most 9 out of 10. Do
as many parts as you deem necessary. Each part is worth 2 point
Math 10B - Calculus of Several Variables II - Winter 2011
March 9, 2011
Practice Final
Name:
There is no need to use calculators on this exam. All electronic devices should be turned o and put away.
The only things you are allowed to have are: a writing u
Math 10B - Calculus of Several Variables II
Graded Homework Problem Solutions
1.
Homework Set 1
Problem (5.1 #10). Calculate the given integral and indicate which region of R3 it gives the volume of:
3
2
2 dxdy.
1
0
Solution.
3
2
2
0
1
2
(2x)|3 dy =
1
2 d
Math 10B - Calculus of Several Variables II - Spring 2011
March 27, 2011
Practice Final
Name:
There are 160 possible points on this exam. A perfect score will be 130 points. There is no need to use calculators
on this exam. All electronic devices should b
Math 10B - Calculus of Several Variables II
Quiz 2
April 15, 2011
Name:
Total
/10
Evaluate the integral:
1
dV.
xyz
[1,e][1,e][1,e]
Solution. The order of integration actually does not matter here (since the region is a cube), so we will proceed as
follows
MATH 10B: Midterm - Sample
There are 5 questions.
No calculators are allowed.
Simplify your answers as far as possible.
(1) Evaluate
(2) Evaluate
Z
Z
0
1
Z
p
2
0
2
x + 2y dxdy .
0
Z
p
sin(x2 ) dxdy
y/2
by changing the order of integration.
(3) Let W be t