Calculus 3 Spring 2012
Written Homework #3
Due 2/10/2012
Chapter 13
1) A Warren Truss is a structure for bearing a weight such as a roof or a bridge with two supports at either end
of a gap. The truss
Tom Pickens
Assignment Section 17.4 due 03/21/2013 at 03:00am MDT
Math2400
1. (1 pt) Sketch each of the vector elds
v1 = 2, 0
v2 = 3, 3 .
and
and their ows. Then use your sketches to match the vector
Tom Pickens
Assignment Sections 16.1 16.2 due 03/07/2013 at 02:59am MST
(36/4)*(sqrt(2*36/4)
(36/8)*(2*sqrt(2*36/4)+2*sqrt(2*36/2)+sqrt(2*36)
1. (1 pt) Values of f (x, y) are shown in the table belo
Tom Pickens
Assignment Sections 20.1 20.2 due 04/25/2013 at 03:00am MDT
1. (1 pt) Consider div
5. (1 pt) Let F = (3a2 x + 4ay2 )i + (4z3 2ay) j (z + 4x2 +
yi x j
.
(x2 + y2 )2
(a) Is this a vector or
Tom Pickens
Assignment Sections 12.3 12.4 due 01/24/2013 at 03:01am MST
Math2400
1. (1 pt) Find an equation for the contour of f (x, y) =
2x2 y + 11x + 10 that goes through the point (3, 1).
Equation:
Tom Pickens
Assignment Section 17.2 due 03/21/2013 at 03:00am MDT
(Enter the times as a comma separated list, or enter none if
there are none.)
Any times when the particle has come to a stop.
times =
Tom Pickens
Assignment Section 17.5 due 04/04/2013 at 03:00am MDT
Math2400
b + -8
c + 16
1. (1 pt) For a sphere parameterized using the spherical coordinates and , describe in words the part of the
Tom Pickens
Assignment Section 16.4 due 03/14/2013 at 03:00am MDT
1. (1 pt) For the regions R below, write R f dA as an iterated
integral in polar coordinates. (Use t for in your expressions.)
With a
Tom Pickens
Assignment Section 13.3 due 02/07/2013 at 03:01am MST
5. (1 pt) Compute the angle between the vectors + + k
i j
and + k.
i j
radians
angle =
(Give your answer in radians, not degrees.)
1
Tom Pickens
Assignment Section 14.8 due 02/21/2013 at 03:00am MST
Math2400
lim f (h, h) =
h0
1. (1 pt) List the points in the xy-plane, if any, at which the
(In each case, enter DNE if the limit does
Tom Pickens
Assignment Section 16.5 due 03/14/2013 at 03:00am MDT
1. (1 pt) Find an equation for the paraboloid z = x2 + y2 in
spherical coordinates. (Enter rho, phi and theta for , and ,
respectively
Tom Pickens
Assignment Section 17.1 due 03/21/2013 at 03:00am MDT
6. (1 pt) (a) Find a vector parallel to the line of intersection
of the planes 5x 5y + 5z = 15 and 2x 5y 5z = 2.
v=
(b) Show that the
Tom Pickens
Assignment Section 17.3 due 03/21/2013 at 03:00am MDT
Math2400
For all graphs, vectors are shown as line segments, with a dot
at the tail of the vector.
1. (1 pt) Consider the vector eld F
Tom Pickens
Assignment Section 16.7 due 03/14/2013 at 03:00am MDT
Math2400
5. (1 pt) Find a number a so that the change of variables
s = x + ay,t = y transforms the integral
R dx dy over the
parallelo
Calculus 3 - Summer 2012
Written Homework #2 Solutions
i
1. Find all vectors v in the plane such that v =
5 and v + =
j
5.
First, express v in coordinates: v = a, b = a + b We now have the two equatio
Midterm 3 Review
Short Answer
2.
Give an example of a non-constant function f(x, y) such that the average value of f over
is 0.
3.
Compute the Riemann sum for the double integral
given grid and choice
Math 2400 Calculus 3, Fall 2014
Homework Set 11
Due: 11/11/14
1. Section 12.9: #12, 14
2. Section 13.1: #24
3. Let x = x, y, z and let c be a positive constant. Dene the vector eld
c
G(x) = 3 x.
|x|
(
Math 2400: Calculus 3, Fall 2014
Homework Set 13
Due date: 12/2/2014
1. Section 13.4 #1, 17.
2. Section 13.5 #5, 16.
3. Use the vector eld
1
1
F = yi + xj
2
2
and Equation 12 (Greens Theorem) in Secti
Math 2400: Calculus 3, Fall 2014
Homework Set 7
Due date: 10/14/2014
1. Section 11.6 #39.
2. Section 11.7 #40.
3. Section 12.1 #3.
4. Let r = x, y, z and let
g(x, y, z) =
1
x2
+ y2 + z2
Show that
g=
Math 2400 Calculus 3, Fall 2014
Homework Set 5
Due: 9/30/14
1. Fin a parametric representation for the plane that contains the lines r = 1t, 2+2t, 5+4t
and r = 2t, 4 t, 9 + 2t .
2. Find a parametric r
Math 2400 Calculus 3, Fall 2014
Homework Set 4
Due: 09/23/14
1. Find the (possibly negative) values of t where the curve
r(t) = t, 0, 2t t2
intersects the paraboloid
z = x2 + y 2 .
2. 10.2: #26
3. Sup
Calculus 3
Notes
KristaKingMath.com
Plotting points in three dimensions
To plot points in three-dimensional coordinate space, well start with a three dimensional
coordinate system, where the x-axis co
Math 2400: Midterm 2 Review
1. Let p0 = (1, 0, 2). In 3-dimensional space, identify the range of each of the following as either
a line, a plane, or neither:
(a) r~1 (t) = p0 + t < 2, 0, 1 >
Answer: T
Name: _ Class: _ Date: _
ID: A
Final Exam Review
Short Answer
(1,-1,0) r=1/2
(3,-2,-2) r=1
1. Find the distance between the sphere (x 1) 2 + (y + 1) 2 + z 2 =
d=sqrt(2^2+1^2+2^2)
d-1-1/2
1
and the sph