MATH 2202 - Quiz 4 (Version 2) Solution
October 2, 2009
NAME_
Use integration to nd the volume of the solid of revolution when the
shaded region pictured below is revolved about the y axis. You may use either
the slab method or the shell method (although
Bindia Mathew
01-13-10
Review for Quiz 1
Hi everyone. Try to attempt all of the exercises in this study guide and
in "An Overview of Integration" before you come to the session tomorrow so
that we can gure out and focus on the areas where you are having t
S. F. Ellermeyer
MATH 2202 - Exam 3 (Version 1) Solutions
November 12, 2010
Name
Instructions. Show all of your work! You will not get full credit if you don include correct
t
notation. In particular, you must write = where needed. Write in complete sente
S. F. Ellermeyer
MATH 2202 Exam 2 (Version 1) Solutions
October 15, 2010
Name
Instructions. This exam contains 5 problems. In giving solutions to these problems, you
must be detailed, use correct notation, and present the solution in an organized way.
1.
S. F. Ellermeyer
MATH 2202 - Exam 3 (Version 2) Solutions
November 12, 2010
Name
Instructions. Show all of your work! You will not get full credit if you don include correct
t
notation. In particular, you must write = where needed. Write in complete sente
MATH 2202 Quiz 3 (Version 2) Solution
September 21, 2009
NAME_
A graph of the curve with parametric equation
x = 3t t3
y = 3t2
is shown below. (The graph that is shown is traced out as t varies from
to 2).
y
2
12
11
10
9
8
7
6
5
4
3
2
1
0
-2
-1
0
1
2
x
Us
MATH 2202 - Quiz 6 (Version 2) Solution
October 26, 2009
NAME_
P
1. Suppose that we have a series 1 an and suppose that we have disn=1
covered that limn!1 an = 1. Does this allow us to conclude anything
P
about the convergence or divergence of the series
MATH 2202 - Quiz 6 (Version 1) Solution
October 26, 2009
NAME_
P
1. Suppose that we have a series 1 an and suppose that we have disn=1
covered that limn!1 an = 0. Does this allow us to conclude anything
P
about the convergence or divergence of the series
MATH 2202 - Quiz 8 (Version 1) Solution
November 18, 2009
NAME_
The MacClaurin series for the function f (x) = ln (1 + x) is
x
1 2 1 3
x + x
2
3
1 4 1 5
x + x
4
5
Explain why. (In other words, show how the coe cients, an , of this power
series are obtaine
MATH 2202 - Quiz 7 (Version 1) Solution
November 11, 2009
NAME_
Find the radius of convergence and the interval of convergence of the
power series
1
Xp
nxn .
n=1
You must show all of your work in detail (well-written).
Answer: The radius of convergence of
MATH 2202 - Quiz 7 (Version 2) Solution
November 11, 2009
NAME_
Find a power series representation for the function
x3
f (x) =
(1 x)2
and determine the radius of convergence of this power series.
Hint: Begin with the fact that
1
1
x
= 1 + x + x2 + x3 +
fo
MATH 2202 Quiz 3 (Version 2) Solution
February 17, 2010
NAME_
When the region pictured in Figure A is revolved about the y axis, we
obtain the solid pictured in Figure B (a bowl with a hole in the bottom).
y = x ? 1 2
y = x ? 1 4
Figure A
Figure B
a) Use
S. F. Ellermeyer
MATH 2202 Exam 3 Solutions July 13, 2005 Name
Instructions. Your work on this exam will be graded according to two criteria: mathematical correctness and clarity of presentation. In other words, you must know what you are doing (mathemati
MATH 2202 Quiz 3 (Version 1) Solution
February 17, 2010
NAME_
When the region pictured in Figure A is revolved about the x axis, we
obtain the solid pictured in Figure B (a cone with a curved interior).
y = x?1
y = x ? 1 4
Figure A
Figure B
a) Use the was
MATH 2202 Quiz 4 (Version 1) Solution
February 24, 2010
NAME_
There are two problems on this quiz. Each problem will be graded separately and
given a score of 0, 4, 10, 16, or 20. The two scores will then be averaged to obtain the
overall quiz score. Plea
MATH 2202 - Quiz 4 (Version 1) Solution
October 2, 2009
NAME_
Use integration to nd the volume of the solid of revolution when the
shaded region pictured below is revolved about the x axis. You may use either
the slab method or the shell method (although
Calculus II - Quiz 7 (Version 2) Solution
NAME_
In answering the two questions on this quiz, the important thing is that you explain
your reasoning correctly and clearly. Write in complete sentences. Use correct
notation. Refer to any necessary convergenc
MATH 2202 Quiz 4 (Version 2) Solution
February 24, 2010
NAME_
There are two problems on this quiz. Each problem will be graded separately and
given a score of 0, 4, 10, 16, or 20. The two scores will then be averaged to obtain the
overall quiz score. Plea
Calculus II - Quiz 7 (Version 1) Solution
NAME_
In answering the two questions on this quiz, the important thing is that you explain
your reasoning correctly and clearly. Write in complete sentences. Use correct
notation. Refer to any necessary convergenc
MATH 2202 Quiz 3 (Version 1) Solution
September 21, 2009
NAME_
Use integration to nd the area of the region that lies between the parabolas y = 12 x2 and y = x2 6.
In order to receive full credit, you must include
a drawing of the region in question
detai
MATH 2202 Quiz 5 (Version 2) Solution
March 22, 2010
NAME: _
Use a partial fraction decomposition to find the sum of the series
k1
4 .
k 2 2k
Include all details of your work.
Solution: By partial fraction decomposition we obtain
4
2 2 .
k
k2
k 2 2k
Thus
Calculus II - Quiz 6 (Version 1) Solution
NAME_
Use either the Integral Test or the Standard Comparison Test or the Limit
Comparison Test to explain why the series
n1
2
n1
diverges.
Solution: Note that for all integers n 1 we have
2 2 2 1.
n
nn
n1
2n
Sinc
Calculus II - Quiz 6 (Version 2) Solution
NAME_
Use either the Integral Test or the Standard Comparison Test or the Limit
Comparison Test to explain why the series
n1
2
2n 1
2
converges.
Solution: Note that for all integers n 1 we have
2
2 2 2 2 12 .
2
2
MATH 2202 - Quiz 2 (Version 2)
January 27, 2010
NAME_
A graph of the function fx x sec 2 x is shown below
f HxL
1.5
x sec2 HxL
1.0
0.5
p
4
1) (Circle the correct choice.) By just looking at this graph, it appears that
/4
0 x sec 2 x dx (is a positive num
MATH 2202 - Quiz 2 (Version 1) January 27, 2010 NAME_ A graph of the function fx x 2 sin2x is shown below
1) (Circle the correct choice.) By just looking at this graph, it appears that 0 x 2 sin2x dx (is a positive number, is a negative number, is zero).
MATH 2202 Quiz 5 (Version 1) Solution
March 22, 2010
NAME: _
Use a partial fraction decomposition to find the sum of the series
k1
6
.
2k 12k 1
Include all details of your work.
Solution: By using partial fraction decomposition we obtain
3
3
6
2k 1
2k 1