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 in the gure below is loaded by weights at points D and
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
elds with the gures below, which show the vector elds a
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 below.
y=3
y = 3.4
y = 3.8
x=1
10
11
12
x = 1.3
11
12
13
Ma
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 a scalar? ?
(b) Calculate it:
div (xyix2j)2 =
+
2 +y
Ma
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:
Correct Answers:
(a)
(b)
(c)
(d)
(e)
(f)
2*y*x2+11*x+
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 =
(Enter the times as a comma separated list, or enter no
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 sphere given
by the restrictions
3. (1 pt) A decorative
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 =
,b=
,
c=
, and d =
,
b d
R f dA = a c f dA, where
d
d
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. (1 pt) Let a, b, c and y be the three dimensional vec
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 xyplane, if any, at which the
(In each case, enter DNE if the limit does not exist.)
Is f continuous at (0, 0)? ?
Is f different
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.)
equation:
Math2400
6. (1 pt) The region W is the con
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 point (1, 1, 1) lies on both planes. Then
nd a vector p
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 = (e1y x) i. Assume
x, y > 0 and decide if
(a) The vec
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
parallelogram R in the xyplane with vertices (0, 0), (10, 0),
(
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 equations
i
j.
v =
i
 a, b 1, 0  =
 a 1, b  =
5
v+ =
j
5

Midterm 3 Review
Short Answer
2.
Give an example of a nonconstant 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 of sample points.
where
where
4.
Evaluate
5.
Evaluate
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
(a) Deduce that G(x) is a conservative eld by showing th
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 Section 13.5 to nd the area of the ellipse
x2 y 2
+ 2 = 1,
a
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=
,
r
.
r 3
(x, y, z) = (0, 0, 0).
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 representation for the part of the sphere x2 + y 2 + z 2
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. Suppose a y is buzzing around a room, and his velocity is
Calculus 3
Notes
KristaKingMath.com
Plotting points in three dimensions
To plot points in threedimensional coordinate space, well start with a three dimensional
coordinate system, where the xaxis comes toward us on the left, the yaxis moves out
toward
Math 2400: Midterm 2 Review
1. Let p0 = (1, 0, 2). In 3dimensional 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: This is a line.
(b) r~2 (t) = p0 + t2 < 2, 0, 1 >
Answer