Math233 Unit 1 IP AIU

MATH233_Unit_1IP_2A.pdf
math233_unit_1ip_2a.pdf

math233_unit_1ip_2a.pdf

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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? ?8
? 2 +1
?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? ?1 F(?).
x
F(x)
0.9
b. Let G(x) =
x
G(x)
5
.
(? -2)2
1.9
0.99
0.999
1
1.001
1.01
1.1
2
2.001
2.01
2.1
Find lim? ?2 G(?).
1.99
1.999
3. Answer the following questions thoroughly based on the given graph of f(x).
Page 1 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?
1
4. Let ?(?) = (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
A(n)
-0.1
-0.01
-0.001
-0.0001
.0001
0.001
0.01
0.1
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:
?(?) =
??
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
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 2 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?
Page 3 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? ?8
? 2 +1
?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? ?1 F(?).
x
F(x)
0.9
b. Let G(x) =
x
G(x)
5
.
(? -2)2
1.9
0.99
0.999
1
1.001
1.01
1.1
2
2.001
2.01
2.1
Find lim? ?2 G(?).
1.99
1.999
3. Answer the following questions thoroughly based on the given graph of f(x).
Page 1 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?
1
4. Let ?(?) = (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
A(n)
-0.1
-0.01
-0.001
-0.0001
.0001
0.001
0.01
0.1
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:
?(?) =
??
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 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 2 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? Page 3 of 3 ... Purchase answer to see full attachment