Mathematics 2433-007
Name (please print)
Examination I
September 19, 2002
I.
Consider the polar equation r = 1 + cos().
(5)
1. In a (, y)-coordinate system, sketch the graph of the Cartesian equation y = 1 + cos().
2. In an (x, y)-coordinate system, sketc
Mathematics 2433-001H
Name (please print)
Examination I
September 21, 2005
I.
(6)
(1)n n2
converges to 0. State the Squeeze Principle for limits of sequences,
1 + n3
and use it to verify that this sequence converges to 0.
The sequence whose nth term is
Th
Mathematics 2433-001H
Name (please print)
Examination III
November 18, 2005
I.
(5)
Find the Taylor series for the function f (x) = x3 at a = 1.
II.
(15)
Use power series to calculate each of the following:
f (1) = 1, f (1) = 3(1)2 = 3, f (1) = 6(1) = 6, f
Mathematics 2433-001H
Name (please print)
Final Examination
December 15, 2005
I.
For the quadric surface:
x2 + y 2 z 2 = 4
(8)
1. In the yz-plane, make a reasonably accurate sketch of the traces with x = k, for appropriate ranges of k.
See graphs download
Math 2433 homework
25. (11/4) 13.3 # 1, 2, 11, 12, 14, 26, 27, as many as needed from 3-10, from 15-20, and
from 23, 24
26. (11/18) 13.3 # 39-42, 51, 52, 58
27. (11/18) 13.4 # 9-12, 17-18, 38, 39(a) (all of these problems use the denition of a b,
not dire
Mathematics 2433-001H
Name (please print)
Examination II
October 24, 2005
I.
(20)
For each of the following series, use standard facts and/or convergence tests to determine whether the
series converges or diverges. Give only brief details, but indicate cl
Mathematics 2433-001H
Name (please print)
Examination III
November 18, 2005
I.
(5)
II.
(15)
Find the Taylor series for the function f (x) = x3 at a = 1.
Use power series to calculate each of the following:
1. lim
x0
2.
n=0
ln(1 + 3x) 3x
.
x2
(1)n 2n
62n (
Mathematics 2433-001H
Name (please print)
Final Examination
December 15, 2005
I.
For the quadric surface:
x2 + y 2 z 2 = 4
(8)
1. In the yz-plane, make a reasonably accurate sketch of the traces with x = k, for appropriate ranges of k.
2. In the xz-plane,
Mathematics 2433-007
Name (please print)
Examination II
October 24, 2002
I.
(6)
For the series
an :
n=1
1. Dene the nth partial sum sn .
2. Dene what it means to say that the series converges.
3. Suppose that sn = n2 . Calculate an .
II.
(6)
Verify that t
Mathematics 2433-007
Name (please print)
Final Examination
December 17, 2002
I.
(4)
Determine whether the planes x + 2y = 4z + 3 and 2x + 13 = 3y + z meet at right angles.
II.
(5)
The lines given by the parametric equations (2 t, 5 + t, 3t) and (11s 9, s
Mathematics 2433-007
Name (please print)
Examination III
November 21, 2002
I.
(6)
The gure to the right is the unit cube in xyz-space. That is,
the set of points (x, y, z) for which 0 x 1, 0 y 1, and
0 z 1.
1. For the bottom face (the one in the xy-plane)
Mathematics 2433-001H
Name (please print)
Examination II
October 24, 2005
I.
(20)
For each of the following series, use standard facts and/or convergence tests to determine whether the
series converges or diverges. Give only brief details, but indicate cl
Mathematics 2433-001H
Name (please print)
Examination I
September 21, 2005
(1)n n2
converges to 0. State the Squeeze Principle for limits of sequences,
1 + n3
and use it to verify that this sequence converges to 0.
I.
(6)
The sequence whose nth term is
II
Review for Third Exam
The third exam will cover sections 12.8, 12.9, 12.10, 13.1, 13.2, and 13.3 of the text. The assignments
on these sections were Assignments 8, 9, and 10.
12.8 We covered this entire section. It includes the denition of what is meant b
Calculus III
Test 3 Solutions
November 22, 2005
1. Sketch the traces of the surface described by the equation below. Each trace graph should have
at least three dierent curves on it.
x2 + y z 2 = 0
The x -traces are parabolas centered on the y -axis, open
Calculus III
Test 2 Solutions
October 25, 2005
1. (a) Use known series to nd a Taylor series (centered at x = 0) for the following indenite
integral. Either write the series in summation notation or nd at least the rst ve non-zero terms
of the series. Als
Calculus III
Test 1 Solutions
September 15, 2005
1. Sketch the curve traced out by the parameter in the following parametric equations:
x = sin t,
y = 1 cos2 t.
Be sure to describe the way in which the curve is traced out as the parameter increases. (You