Name:
Math 247-002 Honors Calculus III
Fall 2012
EXAM 1 REVIEW
9/25/12
1. Let r(t) = t, cos t, sin t .
(a) Compute the unit tangent vector
(b) Compute the unit normal vector
(c) Compute the unit binormal vector
Solution:
r (t) = 1, sin t, cos t
sin t cos
Name:
CWID:
Math 247 Honors Calculus III
Fall 2012
Exam 3
Show all work. Answers without work will receive no credit. No calculators are allowed. There are
10 true/false questions, each worth 4 points. There are 7 multiple choice questions, of which you m
Name:
CWID:
Math 247 Honors Calculus III
Fall 2012
Final Exam
Show all work. Answers without work will receive no credit. No calculators are allowed. There are
15 questions worth 5 points each.
1. Find a tangent vector to the curve r(t) = t cos t, 1 sin t
Name:
CWID:
Math 247 Honors Calculus III
Fall 2012
Final Exam
Show all work. Answers without work will receive no credit. No calculators are allowed. There are
15 questions worth 5 points each.
1. Find a tangent vector to the curve r(t) = t cos t, 1 sin t
Name:
Math 247 Honors Calculus III
Fall 2012
FINAL REVIEW
12/4/12
1. Find the angle between the vectors 1, 1, 2 and 4, 1, 2 .
2. Suppose
r(3) = 1, 2, 1
r (3) = 2, 1, 0
s(3) = 1, 2, 3
s (3) = 2, 2, 5
Compute (r s) (3) and (r s) (3).
3. Find a vector normal
Name:
Math 247 Honors Calculus III
Fall 2012
FINAL REVIEW
12/4/12
1. Find the angle between the vectors 1, 1, 2 and 4, 1, 2 .
Solution: Compute |v | = 6, |w| = 21, and v w = 1. Since v w = |v |w| cos , we obtain =
1
cos1 ( 314 ).
2. Suppose
r(3) = 1, 2, 1
Name:
Math 247 Honors Calculus III
Fall 2012
SURFACE INTEGRALS
11/20/12
1. Let S be the portion of the parabaloid z = 4 x2 y 2 above the xy -plane. Compute the surface area of
S.
Solution: Parameterize S by r(r, ) = r cos , r sin , 4 r2 , 0 r 2, 0 2 . The
Name:
CWID:
Math 247-001 Honors Calculus III
Fall 2014
Exam 4
Show all work. Answers without work will receive no credit. No calculators are allowed on this
exam. There are 110 points available on this exam. Your score will be computed out of 100 in the u
Name:
CWID:
Math 247-001 Honors Calculus III
Spring 2014
Exam 3
Show all work. Answers without work will receive no credit. No calculators are allowed on this
exam. There are 108 points available on this exam. Your score will be computed out of 100 in the
Name:
CWID:
Math 247-001 Honors Calculus III
Fall 2014
Exam 1
Show all work. Answers without work will receive no credit. No calculators are allowed on this
exam. There are 100 possible points on this exam.
Part A
Each question is worth 8 points each. Cho
Name:
CWID:
Math 247-001 Honors Calculus III
Spring 2014
Exam 2
Show all work. Answers without work will receive no credit. No calculators are allowed on this
exam. There are 106 points available on this exam. Your score will be computed out of 100 in the
Name:
CWID:
Math 247-001 Honors Calculus III
Fall 2014
Exam 1
Show all work. Answers without work will receive no credit. No calculators are allowed on this
exam. There are 100 possible points on this exam.
Part A
Each question is worth 8 points each. Cho
Name:
CWID:
Math 247-001 Honors Calculus III
Spring 2014
Exam 2
Show all work. Answers without work will receive no credit. No calculators are allowed on this
exam. There are 106 points available on this exam. Your score will be computed out of 100 in the
Name:
CWID:
Math 247-001 Honors Calculus III
Spring 2014
Exam 3
Show all work. Answers without work will receive no credit. No calculators are allowed on this
exam. There are 108 points available on this exam. Your score will be computed out of 100 in the
Name:
CWID:
Math 247 Honors Calculus III
Fall 2012
Exam 3
Show all work. Answers without work will receive no credit. No calculators are allowed. There are
10 true/false questions, each worth 4 points. There are 7 multiple choice questions, of which you m
Name:
Math 247 Honors Calculus III
Fall 2012
EXAM 3 REVIEW
1. Let F = P, Q be a vector eld dened on a domain D R2 . True/False:
(a) If F is conservative, then
x Q
y P
= 0.
x Q
y P
= 0.
(c) If D is simply connected and F is conservative, then
x Q
(b) If D
Name:
CWID:
Math 247-002 Honors Calculus III
Fall 2012
Exam 1
Choose the best answer. Show all work in this booklet. No calculators are allowed on this exam. There are
11 questions, each worth 9 points.
1. Which of the following vectors is normal to the p
Name:
Math 247-002 Honors Calculus III
Fall 2012
EXAM 1 REVIEW
9/25/12
1. Let r(t) = t, cos t, sin t .
(a) Compute the unit tangent vector
(b) Compute the unit normal vector
(c) Compute the unit binormal vector
2. Find the angle between the vectors 2, 3,
Name:
CWID:
Math 247-002 Honors Calculus III
Fall 2012
Exam 1
Choose the best answer. Show all work in this booklet. No calculators are allowed on this exam. There are
11 questions, each worth 9 points.
1. Which of the following vectors is normal to the p
Name:
CWID:
Math 247-002 Honors Calculus III
Fall 2012
Exam 1
Choose the best answer. Show all work in this booklet. No calculators are allowed on this exam. There are
11 questions, each worth 9 points.
1. Which of the following vectors is normal to the p
Name:
Math 247-002 Honors Calculus III
Fall 2012
EXAM 1 REVIEW
9/25/12
1. Let r(t) = t, cos t, sin t .
(a) Compute the unit tangent vector
(b) Compute the unit normal vector
(c) Compute the unit binormal vector
Solution:
r (t) = 1, sin t, cos t
sin t cos
Name:
Math 247-002 Honors Calculus III
Fall 2012
EXAM 1 REVIEW
9/25/12
1. Let r(t) = t, cos t, sin t .
(a) Compute the unit tangent vector
(b) Compute the unit normal vector
(c) Compute the unit binormal vector
2. Find the angle between the vectors 2, 3,
Line integrals
October 24, 2012
Compute
(1, 1)
C
x 2 dx +
1. 0
2.
3.
4.
1
3
1
2
2
3
5. 1
6. Something else
7. I dont know
x y
3
dy along the straight line from (0, 0) to
Compute C x 2 dx + x y dy along the path in a line from (0, 0) to
3
(1, 0) and then i
Name:
Math 247 Calclulus III
Fall 2012
EXAM 2 REVIEW Optimization & Multiple Integrals
10/29/12
1. Which of the following sets are closed and bounded?
(a) cfw_(x, y ) | x2 + y 2 < 1
(b) cfw_(x, y ) | x2 + y 2 1
(c) cfw_(x, y ) | x2 + y 4 1
(d) cfw_(x, y )
Name:
Math 247 Calclulus III
Fall 2012
EXAM 2 REVIEW Optimization & Multiple Integrals
10/29/12
1. Which of the following sets are closed and bounded?
[(a)]
1. cfw_(x, y ) | x2 + y 2 < 1
2. cfw_(x, y ) | x2 + y 2 1
3. cfw_(x, y ) | x2 + y 4 1
4. cfw_(x, y
Name:
CWID:
Math 247-002 Honors Calculus III
Fall 2012
Exam 1
Choose the best answer. Show all work in this booklet. No calculators are allowed on this exam. There are
11 questions, each worth 9 points.
1. Which of the following vectors is normal to the p
Name:
CWID:
Math 247-002 Honors Calculus III
Fall 2012
Exam 1
Choose the best answer. Show all work in this booklet. No calculators are allowed on this exam. There are
11 questions, each worth 9 points.
1. Which of the following vectors is normal to the p
Name:
CWID:
Math 247-002 Honors Calculus III
Fall 2012
Exam 2
Choose the best answer. Show all work in this booklet. No calculators are allowed on this exam. There are
12 questions, each worth 8 points. You need only work 10 of the 12 questions, although
Name:
CWID:
Math 247-002 Honors Calculus III
Fall 2012
Exam 2
Choose the best answer. Show all work in this booklet. No calculators are allowed on this exam. There are
12 questions, each worth 8 points. You need only work 10 of the 12 questions, although
Name:
CWID:
Math 247-002 Honors Calculus III
Fall 2012
Exam 1
Choose the best answer. Show all work in this booklet. No calculators are allowed on this exam. There are
11 questions, each worth 9 points.
1. Which of the following vectors is normal to the p