Calculus III: Practice Midterm Exam 2
Fall 2012
Name:
Section:
Instructions
This exam consists of 9 pages, including this one. If pages are missing, let the examiner(s) know right away.
Do not unstaple pages.
Show all relevant work. A solution without
MATH V1201 CALCULUS III SECTIONS 4 AND 5
PROF. ADAM KNAPP
HOMEWORK SET 1 SOLUTION
YINGHUI WANG
(A)
Proof. The nth roots of 1 are
1, z, z 2 , z 3 , , z n1 ,
2i
where z = e n = 1.
Since z n = 1 and z = 1, we have
zn 1
0=
= 1 + z + z 2 + z 3 + + z n1 .
z1
He
Exam , :
, April
,
Exam
Linear Algebra, Dave Bayer, :
, April
,
Name:
Uni:
[1]
[2]
[3]
[4]
[5]
Total
If you need more that one page for a problem, clearly indicate on each page where to look next for
your work.
[1] Compute the determinant of the matrix
1
Exam , Alternate, April
,
Exam
Linear Algebra, Dave Bayer, Alternate, April
,
Name:
Uni:
[1]
[2]
[3]
[4]
[5]
Total
If you need more that one page for a problem, clearly indicate on each page where to look next for
your work.
[1] Compute the determinant of
Practice Problems
Linear Algebra, Dave Bayer, February 12, 2011
These are supplemental practice problems for our rst exam.
[1] Find a system of equations having as solution set the following ane subspace of R4 .
w
1
3
5
x
2
4
6
= + s + t
y
0
1
0
z
0
0
1
Practice Problems
Linear Algebra, Dave Bayer, February 12, 2011
These are supplemental practice problems for our rst exam.
[1] Find a system of equations having as solution set the following ane subspace of R4 .
w
1
3
5
x
2
4
6
= + s + t
y
0
1
0
z
0
0
1
Calculus III: Practice Midterm Exam 1
Fall 2012
Name:
Section:
Instructions
This exam consists of 7 pages, including this one. If pages are missing, let the examiner(s) know right away.
Do not unstaple pages.
Show all relevant work. A solution without
Calculus III: Practice Midterm Exam 3
December 10, 2012
Name:
Section:
Instructions
This exam consists of 9 pages, including this one. If pages are missing, let the examiner(s) know right away.
Do not unstaple pages.
Show all relevant work. A solution
MIDTERM #1 REVIEW
Note: I have tried to include what you should know, but I may have overlooked something.
If I lectured in class on a topic, or if it came up in the homework, you are responsible for
understanding it (regardless of whether or not it shows
FINAL EXAM REVIEW
Note: I have tried to include what you should know, but I may have overlooked something.
If I lectured in class on a topic, or if it came up in the homework, you are responsible for
understanding it (regardless of whether or not it shows
MIDTERM #2 REVIEW
Note: I have tried to include what you should know, but I may have overlooked something.
If I lectured in class on a topic, or if it came up in the homework, you are responsible for
understanding it (regardless of whether or not it shows
w
10.13§r§:3,7r/6<6e:5¢r/6
48.
Seem) 12.:
6. (a) In E2, the e nation a: : 4 re resents a line arallel to
q 9 P
the yaxis. In 1313, the equation x = 4 represents the
set y, z) I a: = 4}, the set ofall points whose
ac-coardinate is 4. This is the
:SGCHCY\qZl
m. x 9 2
y? is dened only when x - y 0 <2?
h?
2
y 2
x e Eylfilwl c.» §x££yslwl~80
[A
the domain of f is y) I
wkiyil}
y
3! m Ix x]
yn
y m lx|
18, vi? + 25 3:2 y3 is dened only when 3,; 3: 0 anci
Id
25
PRACTICE MIDTERM I
1) (10 pts) If v w = 1, 2, 3 and v w = 2, nd tan , where is the angle between
two vectors.
2) (10 pts) Find the volume of parallelepiped determined by vectors 1, 2, 3 , 1, 0, 1 ,
1, 1, 1 .
3) (20 pts) Find the plane perpendicular to the
Exam ,
:
, April
,
Exam
Linear Algebra, Dave Bayer,
:
, April
,
Name:
Uni:
[1]
[2]
[3]
[4]
[5]
Total
If you need more that one page for a problem, clearly indicate on each page where to look next for
your work.
[1] Compute the determinant of the matrix
0
Exam , Alternate, March
,
Exam
Linear Algebra, Dave Bayer, Alternate, March
,
Name:
Uni:
[1]
[2]
[3]
[4]
[5]
Total
If you need more that one page for a problem, clearly indicate on each page where to look next for
your work.
[1] Find a basis for the set o
Exam , :
, March
,
Exam
Linear Algebra, Dave Bayer, :
, March
,
Name:
Uni:
[1]
[2]
[3]
[4]
[5]
Total
If you need more that one page for a problem, clearly indicate on each page where to look next for
your work.
[1] Find a basis for the set of solutions to
Exam ,
:
, February
,
Exam
Linear Algebra, Dave Bayer,
:
[1]
, February
[2]
[3]
,
[4]
[5]
Total
If you need more that one page for a problem, clearly indicate on each page where to look next for
your work.
[1] Using matrix multiplication, count the number