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 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 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 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 14.3 due 02/14/2013 at 03:00am MST
the difference quotient with values taken from the second column and row from the second table. That is, do not calculate the
actual partial derivatives of the function.)
f (x, y)
Now, use
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 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),
(
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 14.5 due 02/14/2013 at 03:00am MST
1. (1 pt) Find the gradient of the function f (x, y, z) =
5xey sin(2z).
grad f =
Math2400
8. (1 pt) Find an equation of the tangent plane to the surface
23
z = 5x+y at the point (4, 3, 1).
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 16.4 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 14.6 due 02/21/2013 at 03:00am MST
6. (1 pt) Corn production, C, is a function of rainfall, R (in
inches), and temperature, T (in degrees C). The rst gure below shows how rainfall is predicted to vary with time because
of gl
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
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
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

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
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
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
Tom Pickens
Assignment Section 13.4 due 02/07/2013 at 03:02am MST
1. (1 pt) Consider the planes given by the equations
Math2400
6. (1 pt) Let P = (0, 1, 0), Q = (1, 1, 2), R = (1, 1, 1).
Find
(a) The area of the triangle PQR.
area =
(b) The equation for a