American River College Mathematics Department
Math 401
Spring 2012
Calculus II
COURSE CODE 11255
MWF 11:0512:35
Room 166
INSTRUCTOR
Glenn Pico
OFFICE
Howard Hall Office 118
OFFICE HOURS
Phone
(916)4848963
M9:3010, TTH 10:3011:30, W 2:303:30
TH 2:303
Math 401
Homework
Name:_
Improper Integrals
1.
Evaluate each improper integral.
2. Use the Comparison Test to determine whether each improper integral converges or diverges
(
)
( )
(Hint: compare
with
on
)
3. Find the area of the region that is bounded by
Simpsons Rule
Another way to approximate definite integrals such as ( )
uses parabolas
instead of straight line segments to approximate the curves. This method is known
as Simpsons Rule. To use Simpsons Rule, we will need a regular partition of
with an ev
Math 401
Integration Practice
Name:_
Integration of trig functions/trig substitution
Problem 1
I
IV
VIII
Evaluation each integral
II
VI
III
IX
VII
Problem 2 Evaluate each integral using an appropriate trig substitution
I
IV
VII
II
V
VIII
III
(
)
(
Math 401
Sequences
Name:_
Work the problems on a separate piece of paper and staple to this one and make sure your work is
neat and complete. You will likely need help on some of these problems, so please come and talk to
me if you get stuck.
Problem 1 De
Exam 3 Review (Chapter 8)
Math 401Calculus II
Finishing the review does not imply you are ready for the exam. This review is to help you find where you
need more practice. You should study your notes and homework, and you may wish to find similar
problem
Math 401
Key
Exam II Review
This key contains answers from other textbooks, other worksheets and midnight calculations and
hence may include errata or plain old fashion typos. Unfortunately, there are limited resources on this
planet, and we were not able
Answers to Exam 3 Review
1) 0, 2, 15, 679
2) a. (i) 6, 7;
Math 401Calculus II
(ii) a1 = 1; an+1 = (1)n(an + 1)
b. (i) 36, 49
(ii) a1 = 1; an+1 =
(iii) an = (1)n+1 n
an 1
2
(iii) an = n2
1
1 1
3) a. 1, 2 , 3 , 4 ,. which converges to 0
b. 100 ,100 ,100 ,
Math 401
Exam 3
Name:_
Show all work on the problems Each problem is worth 12 points
Problem 1 Find the limit of the following sequences as
.
a
( 2 n 1) arctan n
3
n 3 1
b.
cos n
3n
No graphing calculators
or determine that the limit does not exist.
(H
.Math 401
Exam 4
Show all work on the problems
Name:_
Problem 1 Write the following power series in summation (sigma) notation.
x 2 x 4 x 6 x8 x10
.
.
3
6 18 72 360
Problem 2
series.
a.
Determine the radius of convergence and interval of convergence of
Math 401
Exam 2
Name:_
Show all work
Problem 1 Evaluate the improper integral
Problem 2 Evaluate the improper integral
Problem 3 Use the Comparison Test to show that the improper integral converges.
Problem 4 Find both the velocity function and the positi
Math 401
Exam 1
Fall 2011
Show all work on the problems
In problems 110 evaluate each integral.
1. (
)
2.
3.
Name:_
No graphing calculator, notes or text
4.
5.
( )
6.
7.
8. (
)
9. (
)
10.
Extra Credit Each problem is worth 5 points extra credit (i
Math 401
Review of Calculus I Integration
Name:_
Problem 1 Evaluate each indefinite integral
(
(
(
)
)
)
(
)
Problem 2 Evaluate each definite integral
(
)
(Hint: think area)


(
)
1
1 x 2 dx
1
cosxdx
0
10
10x x 2 dx
0
8
1
3
x (x 1)dx
[Hint: Comple
Answers to Exam 4 Review
Math 401Calculus II
ln x
1) a. Letting f ( x ) 2 and taking the derivative, we can show that f(x) < 0 for large xvalues, so the
x
terms of the sequence are decreasing. Also, two applications of LHopitals Rule show that the
limit
Exam 4 Review (Chapter 9)
Math 401Calculus II
Finishing the review does not imply you are ready for the exam. This review is to help you find where you
need more practice. You should study your notes and homework, and you may wish to find similar
problem
Math 410
Section 4.4 Basis
cfw_
Definition 1 Let be a vector space and
from . The we say that is a basis for if
I
II
a finite set of vectors
is linearly independent.
( )
.
In the case where there is a finite basis, then we say that
is finitedimensional
S4.1 Real Vector Spaces
In this section, we look at a generalization of
and see that
larger class of sets and these sets are called real vector spaces.
is part of a
Definition 1 Let be a nonempty set of objects that is closed under some
defined addition a
S3.4 Cross Products and Parametric Curves in
Parametric Equation of a Line in
and is parallel to a given vector
that passes through a given point
, where
Parametric Equation of a plane that passes a given point
noncollinear vectors
is
and is parallel to t
Section 3.1 Vectors in
Component form
cfw_(
)
cfw_(
2space
)
3space
cfw_(
)
nspace
In component form we think of vectors as having initial point at the origin and
terminal point at the given ntuple
Vector Arithmetic
(
Let
scalar.
)
(
) be vectors i
Section 2.3 Properties of Determinants and Cramers Rule
Lemma 1 Let
(
)
be an elementary
( )
Then
( ).
From this lemma it follows that if
and
then
(
)
( )
is a sequence of
(
(
)
)
(
)
( ).
( )
Theorem 1
If
Theorem 2
Let
(
)
( )
of the same size. Then
( )
Math 410 Section 1.6 Linear Systems and Invertible Matrices
Definitions and Theorems
Theorem 1 A system of linear equations has zero, one or infinitely many solutions.
Theorem 2 If is an invertible
then for each
system of equations determined by the matri
Section 1.7 Diagonal, Triangular and Symmetric Matrices
Lecture Notes
Definition `1 A square matrix in which all the entries off of the main diagonal are zero is said to
be a diagonal matrix.
Examples of diagonal matrices: [
]
[
]
[
]
Diagonal matrices ma
Section 1.5
Definitions and Theorems
Definition 1 Two matrices
are said to be row equivalent, denoted
be obtained from the other by a sequence of elementary row operations.
For example, [
]
[
if either can
] (just add the first row to the second in first
Section 2.1 Determinants by Cofactor Expansion
Lecture Outline
Determinant of a
[
Let
( )
]. Then
We can also write  


.
Definition of Minors and Cofactors
If
is a square matrix, then the minor of entry
determinant of the submatrix that remains when
Section 1.4
Definitions and Theorems
Theorem 1 Let
Assume that the size of the matrices are
compatible so that all indicated operations are defined. Then we have:
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
(
(
(
)
)
(
(
)
)
)
(
)
(
)
(
)
(
(
)
)
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