Name
Quiz 2
Calculus III 3450:223003 Dr. Norfolk January 21, 2011
Show your work. Unless otherwise specied, give exact answers.
1. Find the exact angle between the vectors a = i j and b =< 1, 2, 2 >.
Name
Homework #1 Due :
Calculus III 3450:223 Dr. Norfolk
1. Find the centre and radius of the sphere with equation
2x2 + 2z 2 6y = 5x 2y 2 + 7z + 9
2. Consider the intersection of the sphere (x 3)2 +
Name
Homework #3 Due :
Calculus III 3450:223 Dr. Norfolk
1. Find the domain of the function r(t) =< sin1
1t
2
, tan(3t2 ), ln(ln t) >.
2. Find the equation of the quadric surface on which the curve r
Name
Homework #5 Due:
Calculus III 3450:223 Dr. Norfolk
1. Find and sketch the domain of f (x, y) =
x2 + y 2 1 + ln(4 x2 y 2 )
.
x+y
x2 sin2 y
2. Find the limit, or show that it does not exist :
lim
(
Name
Homework #4 Due :
Calculus III 3450:223 Dr. Norfolk
1. Find the length of the curve r(t) = 12ti + 8t3/2 j + 3t2 k, 0 t 1.
2. Let r(t) =< t2 , sin t t cos t, cos t + t sin t >, t 0.
Find the unit
Calculus III
Fall 2005
Due 10/10/2005
Dr. D. P. Story
Assignment #1
1. Find the equations of the planes that are parallel to the plane x + 2y 2z = 1 and two units away from
it. (Hint : Draw a picture
Calculus III
Fall 2005
Name:
Dr. D. P. Story
Quiz #6Section 004
Instructions: (10 points) Solve each of the following problems without error. Show all
details. Box in your answers . Use good notation,
(10pts )
Calculus III
Name:
HW #2Section 004
Fall 2005
Dr. D. P. Story
1. (Find Absolute Max/Min.) Consider the function f (x, y ) = 3x + 2y dened over the closed and bounded
region D = cfw_ (x, y ) :
Calculus III
Fall 2005
Name:
Dr. D. P. Story
Quiz #8Section 004
Instructions: (10 points) Solve each of the following problems without error. Show all
details. Box in your answers . Use good notation,
Name
Homework #2 Due :
Calculus III 3450:223 Dr. Norfolk
1. Let u = 2i + 3j, v = j + 2k and w = i + j + k.
Evaluate u (v w) and (u v) w
2. Find the value of c so that the following lines intersect
x1
Homework #1 (Solutions)
Calculus III 3450:223 Dr. Norfolk
1. Find the centre and radius of the sphere with equation
2x2 + 2z 2 6y = 5x 2y 2 + 7z + 9
Solution: Dividing by 2 and completing the squares
Test Total
Name
Final Exam Calculus III 3450:223003 Dr. Norfolk Monday, May 2, 2011
Show all of your work. Give exact, reasonably-simplied answers.
Greens Theorem:
P dx + Qdy =
C
D
(Qx Py ) dA
F dr =
Name
Quiz 1
Calculus III 3450:223-003 Dr. Norfolk January 14, 2011
Show your work. Unless otherwise specied, give exact answers.
1. Consider the triangle with vertices A(4, 4, 3), B (3, 2, 1) and C (5
Name
Quiz 4
Calculus III 3450:223003 Dr. Norfolk February 4, 2011
Show your work. Unless otherwise specied, give exact answers.
t
1 2
1. Find and simplify r (t), given r(t) =< t tan (t ), sin(cos t),
Name
Quiz 3
Calculus III 3450:223003 Dr. Norfolk January 28, 2011
Show your work. Unless otherwise specied, give exact answers.
1. Find the equation of the plane which passes through P (0, 1, 5), and
Name
Quiz 5
Calculus III 3450:223003 Dr. Norfolk February 18, 2011
Show your work. Unless otherwise specied, give exact answers.
2
x + y2 4
1. Sketch the domain of the function f (x, y ) =
.
ln(x + y
Homework #3 (solutions)
Calculus III 3450:223 Dr. Norfolk
1. Find the domain of the function r(t) =< sin1
1t
2
, tan(3t2 ), ln(ln t) >.
Solution:
1t
1, or 1 t 3.
2
3
5
tan(3t2 ) is dened for 3t2 = ,
Homework #2 (solutions)
Calculus III 3450:223 Dr. Norfolk
1. Let u = 2i + 3j, v = j + 2k and w = i + j + k.
Evaluate u (v w) and (u v) w
Solution:
i
j k
v w = 0 1 2 = 3i + 2j + k
1
1 1
So,
u (v w) =
i
Test Total
Name
Final Exam Calculus III 3450:223004 Dr. Norfolk Monday, May 3, 2010
Show all of your work. Give exact, reasonably-simplied answers.
Greens Theorem:
P dx + Qdy =
C
D
(Qx Py ) dA
F dr =
Calculus III
Fall 2005
Date: 12/05/05
Dr. D. P. Story
Assignment #3 - Solution Notes
1. Set up limits of integration. After carefully drawing the region and examining the various projections, we
get:
Calculus III
Fall 2005
Name:
Dr. D. P. Story
Quiz #1Section 004
Instructions: (10 points) Solve each of the following problems without error. Show all details. Box in
your answers . Use good notation,
Calculus III
Fall 2005
Name:
Dr. D. P. Story
Quiz #3Section 004
Instructions: (10 points) Solve each of the following problems without error. Show all details. Box in
your answers . Use good notation,
Name
Quiz 2
Calculus III 3450:223003 Dr. Norfolk January 21, 2011
Show your work. Unless otherwise specied, give exact answers.
1. Find the exact angle between the vectors a = i j and b =< 1, 2, 2 >.
Name
Quiz 4
Calculus III 3450:223003 Dr. Norfolk February 4, 2011
Show your work. Unless otherwise specied, give exact answers.
t
1 2
1. Find and simplify r (t), given r(t) =< t tan (t ), sin(cos t),
Name
Quiz 5
Calculus III 3450:223003 Dr. Norfolk February 18, 2011
Show your work. Unless otherwise specied, give exact answers.
2
x + y2 4
1. Sketch the domain of the function f (x, y ) =
.
ln(x + y
Name
Quiz 10
Calculus III 3450:223003 Dr. Norfolk April 8, 2011
Show your work. Unless otherwise specied, give exact answers.
1. SET UP BUT DO NOT EVALUATE, the triple integral for the volume of the s
Name
Quiz 11 (take home, due Monday, April 25)
Calculus III 3450:223003 Dr. Norfolk
April 20, 2011
Show your work. Unless otherwise specied, give exact answers.
1. Consider the smooth curve C : r(t) =
Name
Quiz 9
Calculus III 3450:223003 Dr. Norfolk April 1, 2011
Show your work. Unless otherwise specied, give exact answers.
1. Evaluate
R
2 y/x
e dA, where R = [1, 2] [1, 3].
x3
5 points
0
2. Conside
Name
Quiz 8
Calculus III 3450:223003 Dr. Norfolk March 11, 2011
Show your work. Unless otherwise specied, give exact answers.
1. Let f (x, y ) = x4 +
y4
4xy .
256
(a) Show that the only critical poin
Name
Quiz 6
Calculus III 3450:223003 Dr. Norfolk February 25, 2011
Show your work. Unless otherwise specied, give exact answers.
1. Find the rst partial derivatives for the function f (x, y, z ) = xz