Topic: Series
Use MATLAB to find the first 20 partial sums of the series. Graph both the sequence of terms and the
sequence of the partial sums on the same screen. Does it appear that the series is co
Tutorial (Sequences)
An infinite sequence is a function whose domain is a set of whole numbers. MATLAB can work with a
finite number of terms.
1. Graph the first 60 terms of the sequence
4n 2
3n 5 .
Homework Guidelines
Homework will be collected at the beginning of the lecture on the indicated due date and a
specified sample of the exercises will be graded.
The following instructions are essentia
MATLAB
Topic: Optimization Problems
Example:
A rectangular solid with a square base has a surface area of 337.5 square cm. Find the dimensions that
will result in a solid with maximum volume.
Let x be
Finite Geometric Series
Definition
A finite geometric series is a finite series in which each successive term is obtained from the previous
term by multiplying by a fixed number r (common ratio) and n
Homework 4
There are 12 problems in this set. Submit any 9 problems. It is due March 24.
Topic: Techniques of Integration
1. Integrate. Write the appropriate formula. Show each step!
x sin 3xdx
2. Fi
Homework 1
There are 8 problems in this set. Submit any 6 problems. It is due February 24.
Topic: Area between curves
1. Find the area of the shaded region. Provide the appropriate formula. Show your
Homework 2
There are 8 problems in this set. Submit any 5 problems. It is due March 3.
Topic: The Disk Method (with cavities)
1. Find the volume of the solid formed by revolving the given region about
Homework 3
There are 9 problems in this set. Submit any 6 problems. It is due March 10.
Topic: Arc Length
1.
a) Show thatthe arc length between two points x1 , y1 and x2 , y 2 on the graph of the func
MATLAB Project
Topic: Function Analysis
Example: The concentration C of a chemical in the bloodstream t hours after injection into muscle tissue
is C (t )
3t
,t 0 .
27 t 3
Use MATLAB to find the conc
MATLAB Project
Topic: Estimating Limits in MATLAB
For continuous functions it is easy to find a limit because lim f ( x)
x
a
f (a) . Some functions are not
continuous at a point a , but we can still f
MATLAB Project
Topic: Finding Limits in MATLAB (The Squeeze theorem)
Sometimes we can use the Squeeze theorem to find the limit. The original function is squeezed between
two other functions, each of
MATLAB Project
Topic: Related Rates
The radius r of a sphere is increasing at a rate of 3 inches per minute. Use MATLAB to find the
rate of change of the volume when r = 9 inches.
Solution
dr
4
3 inc
MATLAB Project
Topic: Functions and Continuity
Use MATLAB to sketch the graph of the piecewise function. Explain why the function is discontinues at
the given number a.
cos x
f ( x) 0
1 x 2
if
x0
if
MATLAB Project
Topic: Extreme Values
Example:
Use MATLAB to graph the function. Find the absolute extrema on the given interval.
y x 4 2 x 3 x 1;[1,3]
x=-1:0.1:3;
y=x.^4-2*x.^3+x+1;
plot(x,y)
Minimum=
MATLAB Project
Topic: Graphing the function and its derivative in MATLAB
Example: Plot the function f ( x) x 4 3x 2 2 and its derivative on the same plane. Add the plot of
the tangent line at the poin
MATLAB Project
Topic: Derivative, Applications
Example: A population of 500 bacteria is introduced into a culture and grows in number
4t
according to the function P(t ) 500 1
where t is measured in ho
1 st Quiz CSI100
The Corrections System
MULTIPLE CHOICE
1. When all forms of correctional supervision are taken into account, what percent of all adults in
the United States are under some form of cor
Differential Equations
Chapter 1
Boyce, DiPrima and Meade
Elementary Differential Equations 11th edition
INTRODUCTION
What are some examples of
phenomena which involve a rate of
change?
What are some
Math 240
Chapter 4
Sections 4.1 4.5:
Direct Proof and Counterexample
SOME ASSUMPTIONS
1.
3 properties of equality for all objects:
(Reflexivity)
If , then (Symmetry)
If and , then (Transitivity)
2.
K E I 1
MATH 240 EXAM 1
Section I (25 x 4 = 100 points) / 100
Usesets A =cfw_1,4,7,B =cfw_h,j,k,C =cfw_xEZI4SxS 10,and D =Z+forProblemsl11:
1. Howmanyelementsarein BXC? B k; 3 - ~13 50 3x? =-
C, has 7
Math 240
Chapter 3
Sections 3.1 and 3.2:
The Logic of Quantified Statements
Definitions
A predicate is a sentence that contains a finite number of
variables, and becomes a statement when specific val
Math 240:
Discrete Mathematics
Sections 4.6 4.8:
Indirect Methods of Proof
PROOF BY CONTRADICTION
1. Suppose the statement to be proved is false,
i.e., assume that the negation of the
statement is tru
Math 240
Chapter 5
Section 5.1:
Sequences
EXAMPLE: Suppose you wish to count the number of
people in your family tree, counting yourself
as Row 0. How many relatives are in the kth row?
Describe a fun
Imperial Valley College
Math 240
EXAM 1 REVIEW GUIDE
This exam will be based primarily on the exercises at the end of each section of the Epp text, and on in-class examples.
Sections: 1.2, 1.3, 2.1, 2
Math 240
Discrete Mathematics
Sections 5.4 and 5.6
Definitions
DEFINITIONS
A
relation for a sequence
recurrence
is a formula that relates each term to certain of its
predecessors , where with .
The i
Imperial Valley College
Math 240
CHAPTER 2 PRACTICE QUIZ
1.
Negate the following statements:
a.
b.
Dillon likes big butts and he cannot lie.
If you eat pizza before bedtime, then you will have
strange
Imperial Valley College
Math 240
EXAM 2 REVIEW GUIDE
This exam will be based primarily on the exercises at the end of each section of the Epp text, and on in-class examples.
Sections: 4.1, 4.2, 4.3, 4
Imperial Valley College
Math 240
PROJECT 2
You may work alone or in groups of two. If you work with a partner, turn in one project with both names on it.
This project is due at the beginning of class
Imperial Valley College
Math 240
PROJECT 1
You may work alone or in groups of two. If you work with a partner, turn in one project with both names on it.
This project is due at the beginning of class