Page 1 of 3 MATH233 Unit 1: Limits Individual Project Assignment: Version 2A IMPORTANT: Please see Part b of Problem 5 below for special directions. This is mandatory. Note: All work must be shown and explained to receive full credit. 1. Using a graphing utility from the Internet or Excel, graph the following functions. Based on the graphs, estimate the given limit. Make sure to include the graphs in your answer form, and explain how you found your limit estimates. a. lim𝑥 →0 100 50𝑥+1 b. lim𝑥 →∞ 𝑥2+1 𝑥2 2. Find the limit (if it exists) of the following functions by completing the given tables. Round your answers to the nearest ten-thousandths. a. Let F(x) = x + 1. Find lim𝑥 →1F(𝑥). x 0.9 0.99 0.999 1 1.001 1.01 1.1 F(x) b. Let G(x) = 5 (𝑥 −2)2 . Find lim𝑥 →2G(𝑥). x 1.9 1.99 1.999 2 2.001 2.01 2.1 G(x) 3. Answer the following questions thoroughly based on the given graph of f(x). Page 2 of 3 a. Is f(x) continuous at x = −1? b. Is f(x) continuous at x = 2? c. Is f(x) continuous at x = 4? 4. Let 𝐴(𝑛) = (1 + 𝑛) 1 𝑛. The limit of this function as n approaches 0 is a value that is very useful in some business applications. a. Complete the table below by calculating A(n), using the given values of n. Round your answer to the nearest ten-thousandths. n -0.1 -0.01 -0.001 -0.0001 .0001 0.001 0.01 0.1 A(n) b. Based on the table, estimate the following values: i. lim𝑛→0−𝐴(𝑛) ii. lim𝑛→0+𝐴(𝑛) iii. lim𝑛→0 𝐴(𝑛) 5. The cost, C (in millions of dollars) for a software company to seize x% of an illegal version of a gaming software that they developed is modeled by the following function: 𝐶(𝑥) = 𝑀𝑥 50−0.5𝑥 0 ≤ 𝑥 < 100 a. Choose a value of M between 20 and 120 for this function. b. Important: By Wednesday night at midnight, submit a Word document stating only your name and your chosen value for M in Part a. Submit this in the Unit 1 IP submissions area. This submitted Word document will be used to determine the Last Day of Attendance for government reporting purposes. c. Find the cost of seizing 50%, 60%, 70%, 80%, and 90% of the illegal software. d. Find the lim𝑥→100−𝐶(𝑥). Explain briefly what this limit means in terms of the given scenario. 6. A startup company invested $30,000 for the research and development of a new hardware plus an additional $80 expense for each unit produced. The total cost is then modeled by the function 𝐶(𝑥) = 80𝑥 + 30,000, where x is the number of units produced. a. Find the average cost function, A(x), that models the average cost per unit of the hardware. (Use the Internet to research the formula for the average cost function.) b. Find the average cost per unit if 1,000 units, 10,000 units, and 100,000 units of the hardware are produced. Page 3 of 3 c. What is the limit of the average cost as the number of units produced increases? 7. Which intellipath L

1. Page 1 of 3
MATH233 Unit 1: Limits
Individual Project Assignment: Version 2A
IMPORTANT: Please see Part b of Problem 5 below for special
directions. This is mandatory.
Note: All work must be shown and explained to receive full
credit.
1. Using a graphing utility from the Internet or Excel, graph the
following functions. Based on the
graphs, estimate the given limit. Make sure to include the
graphs in your answer form, and
explain how you found your limit estimates.
a. lim� →0
100
50�+1
b. lim� →∞
�2+1
�2

2. 2. Find the limit (if it exists) of the following functions by
completing the given tables. Round your
answers to the nearest ten-thousandths.
a. Let F(x) = x + 1. Find lim� →1F(�).
x 0.9 0.99 0.999 1 1.001 1.01 1.1
F(x)
b. Let G(x) = 5
(� −2)2
. Find lim� →2G(�).
x 1.9 1.99 1.999 2 2.001 2.01 2.1
G(x)
3. Answer the following questions thoroughly based on the
given graph of f(x).
Page 2 of 3

3. a. Is f(x) continuous at x = −1?
b. Is f(x) continuous at x = 2?
c. Is f(x) continuous at x = 4?
4. Let �(�) = (1 + �)
1
�. The limit of this function as n approaches 0 is a value that is
very
useful in some business applications.
a. Complete the table below by calculating A(n), using the
given values of n. Round
your answer to the nearest ten-thousandths.
n -0.1 -0.01 -0.001 -0.0001 .0001 0.001 0.01 0.1
A(n)
b. Based on the table, estimate the following values:
i. lim�→0−�(�)
ii. lim�→0+�(�)
iii. lim�→0 �(�)
5. The cost, C (in millions of dollars) for a software company to
seize x% of an illegal version of
a gaming software that they developed is modeled by the
following function:

4. �(�) = ��
50−0.5�
0 ≤ � < 100
a. Choose a value of M between 20 and 120 for this function.
b. Important: By Wednesday night at midnight, submit a Word
document stating
only your name and your chosen value for M in Part a. Submit
this in the Unit 1
IP submissions area. This submitted Word document will be
used to determine
the Last Day of Attendance for government reporting purposes.
c. Find the cost of seizing 50%, 60%, 70%, 80%, and 90% of the
illegal software.
d. Find the lim�→100−�(�). Explain briefly what this limit
means in terms of the given
scenario.
6. A startup company invested $30,000 for the research and
development of a new hardware
plus an additional $80 expense for each unit produced. The total
cost is then modeled by the
function �(�) = 80� + 30,000, where x is the number of units
produced.
a. Find the average cost function, A(x), that models the average
cost per unit of the

5. hardware. (Use the Internet to research the formula for the
average cost function.)
b. Find the average cost per unit if 1,000 units, 10,000 units,
and 100,000 units of the
hardware are produced.
Page 3 of 3
c. What is the limit of the average cost as the number of units
produced increases?
7. Which intellipath Learning Nodes helped you with this
assignment?
CRJS478-DB3
Name
Class
Date
Professor

6. DNA
DNA or deoxyribonucleic acid is the unique genetic code
found in the genetic material of humans and animals. Upon the
discovery of this unique genetic code, DNA began an incredibly
useful tool for law enforcement. George Mendel was the first
scientist to perform experiments based on human genetics. The
discovery of DNA began with Fredrick Griffith who conducted
experiments and pointed out DNA was the molecule of
inheritance. Oswald Avery was next in advancing DNA when he
was able to definitively prove the inheritance molecule followed
by Watson and Cricks model of DNA, the double helix.
DNA is made up of a complex set of molecules that make up
a unique code that can be identified to one person. DNA is made
up of nucleotides. A nucleotide is made up of three parts: a
phosphate group, a 5 carbon sugar (deoxyribose in DNA), and a
nitrogenous base (Doublie, 1998). Nucleotides arrange
themselves in unique patterns that make-up the DNA code. DNA
is arranged in a ladder like structure known as the double helix.
The process by which DNA replicates is called cell
replication. When cells split however not every cell will create
new DNA. Before new cells can be created the DNA in a cell
must replicate itself in order for the cell to divide (Ophardt,
2003). This process will be dependent whether or not the cell
splitting is a prokaryote or a eukaryote. Each cell that splits will
contains a new and an old strand of DNA. These strands of
DNA wind together with proteins holding it together in order to

7. form the double helix.
The relationship between DNA, genes, and chromosomes
involves the relationship to heredity. Through this relationship
the DNA pattern that is unique to every individual with the
exception of identical twins. Every DNA strand has the genetic
material passed on by former generations and are made of little
chromosomes. DNA analysis allows forensic scientists to
develop a DNA profile that can be used to be match to a
criminal suspect or even the unidentified.
References
Doublie S., Tabor S., Long A., Richardson C., and Ellenberger
T. (1998). Crystal Structure of a
Bacteriophage T7 DNA Replication complex at 2.2 A
Resolution. Nature 391: 251-258.
Ophardt, C. (2003). DNA Replication. Retrieved November 26,
2013 from
http://www.elmhurst.edu/~chm/vchembook/582dnarep.html