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Deck 9: Derivatives
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Question
Use the graph of 
and the given c-value to find 
. 
A) 4
B) 0
C) 2
D) -6
E) does not exist
and the given c-value to find . A) 4
B) 0
C) 2
D) -6
E) does not exist
Question
A graph of 
is shown and a c-value is given. For this problem, use the graph to find 
. 
A) 5
B) -15
C) 0
D) 15
E) does not exist
is shown and a c-value is given. For this problem, use the graph to find . A) 5
B) -15
C) 0
D) 15
E) does not exist
Question
A graph of 
is shown and a c-value is given. For this problem, use the graph to find 
. 
A) 0
B) 5
C) -5
D) -6
E) does not exist
is shown and a c-value is given. For this problem, use the graph to find . A) 0
B) 5
C) -5
D) -6
E) does not exist
Question
A graph of 
is shown and a c-value is given. For this problem, use the graph to find 
. 
A) 0
B) 2
C) -4
D) -6
E) does not exist
is shown and a c-value is given. For this problem, use the graph to find . A) 0
B) 2
C) -4
D) -6
E) does not exist
Question
Use the graph of 
and the given c-value to find 
. 
A) 2
B) -2
C) 6
D) 0
E) does not exist
and the given c-value to find . A) 2
B) -2
C) 6
D) 0
E) does not exist
Question
Use properties of limits and algebraic methods to find the limit, if it exists. 
A) -45
B) 54
C) 45
D) -54
E) does not exist
A) -45
B) 54
C) 45
D) -54
E) does not exist
Question
Complete the table and use it to predict the limit, if it exists. 
A) -5
B) 5
C) -4
D) 4
E) does not exist
A) -5
B) 5
C) -4
D) 4
E) does not exist
Question
A graph of 
is shown and a c-value is given. For this problem, use the graph to find 
. 
A) 5
B) 0
C) -15
D) 15
E) does not exist
is shown and a c-value is given. For this problem, use the graph to find . A) 5
B) 0
C) -15
D) 15
E) does not exist
Question
Use properties of limits and algebraic methods to find 
if the limit exists.
A) 0
B) 10
C) ∞
D) -10
E) 5
if the limit exists. A) 0
B) 10
C) ∞
D) -10
E) 5
Question
Use the graph of 
and the given c-value to find 
. 
A) -8
B) -6
C) 3
D) -4
E) does not exist
and the given c-value to find . A) -8
B) -6
C) 3
D) -4
E) does not exist
Question
Use the graph of 
and the given c-value to find 
. 
A) -6
B) 0
C) 8
D) 2
E) does not exist
and the given c-value to find . A) -6
B) 0
C) 8
D) 2
E) does not exist
Question
Complete the table and use it to predict the limit, if it exists. 
A) 44.0
B) -22.0
C) 22.0
D) -0.5
E) does not exist
A) 44.0
B) -22.0
C) 22.0
D) -0.5
E) does not exist
Question
Use properties of limits and algebraic methods to find the limit, if it exists. 
A) 63
B) 65
C) 60
D) 68
E) does not exist
A) 63
B) 65
C) 60
D) 68
E) does not exist
Question
Use the graph of 
and the given c-value to find 
. 
A) -6
B) 0
C) 2
D) 6
E) does not exist
and the given c-value to find . A) -6
B) 0
C) 2
D) 6
E) does not exist
Question
Use properties of limits and algebraic methods to find the limit, if it exists. 
A)
B)
C)
D)
E) does not exist
A)
B)
C)
D)
E) does not exist
Question
Use properties of limits and algebraic methods to find the limit, if it exists. 
A) 
B)
C)
D)
E) does not exist
A)
B)
C)
D)
E) does not exist
Question
Use the graph of 
and the given c-value to find 
. 
A) -6
B) -5
C) -1
D) 3
E) does not exist
and the given c-value to find . A) -6
B) -5
C) -1
D) 3
E) does not exist
Question
Use properties of limits and algebraic methods to find the limit, if it exists. 
A)
B) -3
C)
D)
E) does not exist
A)
B) -3
C)
D)
E) does not exist
Question
Use the graph of 
and the given c-value to find 
. 
A) -6
B) -9
C) -1
D) 3
E) does not exist
and the given c-value to find . A) -6
B) -9
C) -1
D) 3
E) does not exist
Question
Use the graph of 
and the given c-value to find 
. 
A) -6
B) -7
C) 3
D) -5
E) does not exist
and the given c-value to find . A) -6
B) -7
C) 3
D) -5
E) does not exist
Question
If 
and 
, find 
.
A)
B)
C) -10
D)
E) does not exist
and , find . A)
B)
C) -10
D)
E) does not exist
Question
Determine whether the function is continuous or discontinuous at the given x-value. 
A) continuous
B) discontinuous
A) continuous
B) discontinuous
Question
For the given x-value, use the figure to determine whether the function is continuous or discontinuous at that x-value. 
A) discontinuous
B) continuous
A) discontinuous
B) continuous
Question
If 
and 
, find 
.
A) 20
B) 6
C) -2
D) -14
E) does not exist
and , find . A) 20
B) 6
C) -2
D) -14
E) does not exist
Question
Determine whether the given function is continuous. If it is not, identify where it is discontinuous. 
A) discontinuous at
B) discontinuous at
C) discontinuous at
D) discontinuous at
E) continuous everywhere
A) discontinuous at
B) discontinuous at
C) discontinuous at
D) discontinuous at
E) continuous everywhere
Question
Use properties of limits and algebraic methods to find the limit, if it exists. 
A) 0
B) -2
C) 2
D) 7
E) does not exist
A) 0
B) -2
C) 2
D) 7
E) does not exist
Question
Suppose that the cost C in dollars of obtaining water that contains p percent impurities is given by 
. Find 
, if it exists.
A) $0
B) $13
C) $117
D) $1,300
E) does not exist
. Find , if it exists. A) $0
B) $13
C) $117
D) $1,300
E) does not exist
Question
A certain calling card costs 6.1 cents per minute to make a call, rounded up to the nearest minute. However, when the card is used at a pay phone, there is an additional 61 cent connection fee. If 
is the charge from a pay phone for a call lasting t minutes, create a table of charges for calls lasting close to 1 minute and use it to find the following limit, if it exists. Round your answer to the nearest cent. 
A) $0
B) $0.61
C) $0.73
D) $0.67
E) does not exist
is the charge from a pay phone for a call lasting t minutes, create a table of charges for calls lasting close to 1 minute and use it to find the following limit, if it exists. Round your answer to the nearest cent. A) $0
B) $0.61
C) $0.73
D) $0.67
E) does not exist
Question
Use properties of limits and algebraic methods to find the limit, if it exists. 
A) 0
B)
C)
D)
E) does not exist
A) 0
B)
C)
D)
E) does not exist
Question
A certain calling card costs 5.2 cents per minute to make a call, rounded up to the nearest minute. However, when the card is used at a pay phone, there is an additional 52 cent connection fee. If 
is the charge from a pay phone for a call lasting t minutes, create a table of charges for calls lasting close to 1 minute and use it to find the following limit, if it exists. Round your answer to the nearest cent. 
A) $0
B) $0.45
C) $0.57
D) $0.44
E) does not exist
is the charge from a pay phone for a call lasting t minutes, create a table of charges for calls lasting close to 1 minute and use it to find the following limit, if it exists. Round your answer to the nearest cent. A) $0
B) $0.45
C) $0.57
D) $0.44
E) does not exist
Question
Graph the function with a graphing utility and use it to predict the limit. Check your work either by using the table feature of the graphing utility or by finding the limit algebraically. 
A)
B) 18
C)
D) 0
E) does not exist
A)
B) 18
C)
D) 0
E) does not exist
Question
Graph the function with a graphing utility and use it to predict the limit. Check your work either by using the table feature of the graphing utility or by finding the limit algebraically. 
A) 10
B) 3
C)
D) 0
E) does not exist
A) 10
B) 3
C)
D) 0
E) does not exist
Question
If 
and 
, find 
.
A) -106
B) -96
C) -81
D) 0
E) does not exist
and , find . A) -106
B) -96
C) -81
D) 0
E) does not exist
Question
A certain calling card costs 6.8 cents per minute to make a call, rounded up to the nearest minute. However, when the card is used at a pay phone, there is an additional 68 cent connection fee. If 
is the charge from a pay phone for a call lasting t minutes, create a table of charges for calls lasting close to 1 minute and use it to find the following limit, if it exists. Round your answer to the nearest cent. 
A) $0
B) $0.68
C) $0.75
D) $0.82
E) does not exist
is the charge from a pay phone for a call lasting t minutes, create a table of charges for calls lasting close to 1 minute and use it to find the following limit, if it exists. Round your answer to the nearest cent. A) $0
B) $0.68
C) $0.75
D) $0.82
E) does not exist
Question
Suppose that the cost C in dollars of obtaining water that contains p percent impurities is given by 
. Find 
, if it exists.
A) $0
B) $20
C) $200
D) $2,000
E) does not exist
. Find , if it exists. A) $0
B) $20
C) $200
D) $2,000
E) does not exist
Question
Determine whether the function is continuous or discontinuous at the given x-value. 
A) discontinuous
B) continuous
A) discontinuous
B) continuous
Question
If the revenue for a product (in dollars) is 
, and the average revenue per unit is 
, 
, find 
.
A) $900 per unit
B) $0.7 per unit
C) $90 per unit
D) $0 per unit
E) does not exist
, and the average revenue per unit is , , find . A) $900 per unit
B) $0.7 per unit
C) $90 per unit
D) $0 per unit
E) does not exist
Question
Graph the function with a graphing utility and use it to predict the limit. Check your work either by using the table feature of the graphing utility or by finding the limit algebraically. 
A) 0
B) 9
C)
D)
E) does not exist
A) 0
B) 9
C)
D)
E) does not exist
Question
If the revenue for a product (in dollars) is 
and the average revenue per unit is 
, 
, find 
.
A) $520 per unit
B) $545 per unit
C) $530 per unit
D) $0 per unit
E) does not exist
and the average revenue per unit is , , find . A) $520 per unit
B) $545 per unit
C) $530 per unit
D) $0 per unit
E) does not exist
Question
If the profit function for a product is given by 
, find 
.
A) -3,600
B) -1,600
C) -2,725
D) -4,100
E) does not exist
, find . A) -3,600
B) -1,600
C) -2,725
D) -4,100
E) does not exist
Question
Suppose that the cost C of removing p percent of the particulate pollution from the exhaust gases at an industrial site is given by 
. Describe any discontinuities for C(p). Explain what each discontinuity means.
A) C(p) is discontinuous at
. This means that not all pollution can be removed.
B) C(p) is discontinuous at
. This means that none of the pollution can be removed.
C) C(p) is continuous everywhere.
D) C(p) is discontinuous at
. This means that not all pollution can be removed.
E) C(p) is discontinuous at
. This means that none of the pollution can be removed.
. Describe any discontinuities for C(p). Explain what each discontinuity means. A) C(p) is discontinuous at
. This means that not all pollution can be removed.B) C(p) is discontinuous at
. This means that none of the pollution can be removed.C) C(p) is continuous everywhere.
D) C(p) is discontinuous at
. This means that not all pollution can be removed.E) C(p) is discontinuous at
. This means that none of the pollution can be removed. Question
Use analytic methods to evaluate the limit and determine which type of asymptote (if any) it represents. You can verify your conclusion by graphing the function with a graphing utility, if one is available. 
A) limit = 10, horizontal asymptote
B) limit = 10, vertical asymptote
C) limit = 4, horizontal asymptote
D) limit = 4, vertical asymptote
E) does not exist, no asymptote
A) limit = 10, horizontal asymptote
B) limit = 10, vertical asymptote
C) limit = 4, horizontal asymptote
D) limit = 4, vertical asymptote
E) does not exist, no asymptote
Question
Suppose that the average number of minutes M that it takes a new employee to assemble one unit of a product is given by 
, where t is the number of days on the job. Is this function continuous for all 
, where t is the number of days on the job. Is this function continuous for all Question
Graph the function using a window with 
and 
. What does the graph indicate about 
A) -5
B) 5
C) 30
D) 0
E) does not exist
and . What does the graph indicate about A) -5
B) 5
C) 30
D) 0
E) does not exist
Question
Use analytic methods to find the limit as 
for the given function. 
A) -1500
B) 1500
C) -620
D) 620
E) does not exist
for the given function. A) -1500
B) 1500
C) -620
D) 620
E) does not exist
Question
Suppose that the average number of minutes M that it takes a new employee to assemble one unit of a product is given by 
, where t is the number of days on the job. What is the domain for this application?
A)
B)
C)
D)
E)
, where t is the number of days on the job. What is the domain for this application? A)
B)
C)
D)
E)
Question
Determine whether the given function is continuous. If it is not, identify where it is discontinuous and which condition fails to hold. You can verify your conclusions by graphing the function with a graphing utility, if one is available. 
A) discontinuous at
B) discontinuous at
C) discontinuous at
D) discontinuous at
E) continuous everywhere
A) discontinuous at
B) discontinuous at
C) discontinuous at
D) discontinuous at
E) continuous everywhere
Question
This problem contains a function and its graph, where 
. Use the graph to determine, as well as you can, 
. Check your conclusion by using the function to determine 
analytically. 
A) 3
B) 0
C) 4
D) 1
E) does not exist
. Use the graph to determine, as well as you can, . Check your conclusion by using the function to determine analytically. A) 3
B) 0
C) 4
D) 1
E) does not exist
Question
This problem contains a function and its graph, where 
. Use the graph to determine, as well as you can, the vertical asymptote. Check your conclusion by using the function to determine the vertical asymptote analytically. 
A)
B)
C)
D)
E) no vertical asymptote
. Use the graph to determine, as well as you can, the vertical asymptote. Check your conclusion by using the function to determine the vertical asymptote analytically. A)
B)
C)
D)
E) no vertical asymptote
Question
Determine whether the given function is continuous. If it is not, identify where it is discontinuous. You can verify your conclusions by graphing the function with a graphing utility, if one is available. 
A) discontinuous at
B) discontinuous at
C) discontinuous at
D) discontinuous at
E) continuous everywhere
A) discontinuous at
B) discontinuous at
C) discontinuous at
D) discontinuous at
E) continuous everywhere
Question
This problem contains a function and its graph, where 
. Use the graph to determine, as well as you can, the horizontal asymptote. Check your conclusion by using the function to determine the horizontal asymptote analytically. 
A)
B)
C)
D)
E)
. Use the graph to determine, as well as you can, the horizontal asymptote. Check your conclusion by using the function to determine the horizontal asymptote analytically. A)
B)
C)
D)
E)
Question
Use analytic methods to find the limit as 
for the given function. 
A) 920
B) 240
C) -920
D) -240
E) does not exist
for the given function. A) 920
B) 240
C) -920
D) -240
E) does not exist
Question
Use analytic methods to find any point of discontinuity for the given function. 
A)
B)
C)
D)
E) continuous everywhere
A)
B)
C)
D)
E) continuous everywhere
Question
Suppose that the average number of minutes M that it takes a new employee to assemble one unit of a product is given by 
, where t is the number of days on the job. Is this function continuous for all values of t?
, where t is the number of days on the job. Is this function continuous for all values of t? Question
Determine whether the given function 
is continuous. If 
is not continuous, identify where it is discontinuous and which condition(s) fails to hold.
A)
is discontinuous at 
since 
is not defined and 
does not exist.
B)
is discontinuous at 
since 
is not defined and 
does not exist.
C)
is discontinuous at 
since 
is not defined and 
does not exist.
D)
is continuous.
E)
is discontinuous at 
since 
is not defined and 
does not exist.
is continuous. If is not continuous, identify where it is discontinuous and which condition(s) fails to hold. A)
is discontinuous at since is not defined and does not exist.B)
is discontinuous at since is not defined and does not exist.C)
is discontinuous at since is not defined and does not exist.D)
is continuous.E)
is discontinuous at since is not defined and does not exist. Question
Use a table utility with x-values larger than 10,000 to investigate 
. What does the table indicate about 
? 
A) -3
B) 3
C) 6
D) 0
E) does not exist
. What does the table indicate about ? A) -3
B) 3
C) 6
D) 0
E) does not exist
Question
This problem contains a function and its graph, where 
. Use the graph to determine, as well as you can, 
. Check your conclusion by using the function to determine 
analytically. 
A) 4
B) 1
C) 3
D) 0
E) does not exist
. Use the graph to determine, as well as you can, . Check your conclusion by using the function to determine analytically. A) 4
B) 1
C) 3
D) 0
E) does not exist
Question
Use analytic methods to evaluate the limit and determine which type of asymptote (if any) it represents. You can verify your conclusion by graphing the function with a graphing utility, if one is available. 
A) limit = 0, vertical asymptote
B) limit = 0, horizontal asymptote
C) limit = 2, horizontal asymptote
D) limit = 2, vertical asymptote
E) does not exist
A) limit = 0, vertical asymptote
B) limit = 0, horizontal asymptote
C) limit = 2, horizontal asymptote
D) limit = 2, vertical asymptote
E) does not exist
Question
Use analytic methods to evaluate the limit and determine which type of asymptote (if any) it represents. You can verify your conclusion by graphing the function with a graphing utility, if one is available. 
A) limit = 4, vertical asymptote
B) limit = 8, horizontal asymptote
C) limit = 8, vertical asymptote
D) limit = 4, horizontal asymptote
E) does not exist
A) limit = 4, vertical asymptote
B) limit = 8, horizontal asymptote
C) limit = 8, vertical asymptote
D) limit = 4, horizontal asymptote
E) does not exist
Question
Suppose that the average number of minutes M that it takes a new employee to assemble one unit of a product is given by 
, where t is the number of days on the job. Is this function continuous at 
, where t is the number of days on the job. Is this function continuous at Question
For the function in this problem, approximate 
by using the numerical derivative feature of a graphing utility. Round your answer to three decimal places. 
A) -0.298
B) -0.421
C) -0.544
D) -0.187
E) -0.655
by using the numerical derivative feature of a graphing utility. Round your answer to three decimal places. A) -0.298
B) -0.421
C) -0.544
D) -0.187
E) -0.655
Question
For the given function, find the average rate of change over the specified interval. 
over 
A) 0
B) 4
C) 2
D) -17
E) 17
over A) 0
B) 4
C) 2
D) -17
E) 17
Question
For the function in this problem, find the instantaneous rate of change of the function at the given value. 
; 
A) 18
B) 6
C) 10
D) 14
E) 13
; A) 18
B) 6
C) 10
D) 14
E) 13
Question
The monthly charge in dollars for x kilowatt-hours (kWh) of electricity used by a residential consumer of Excelsior Electric Membership Corporation from November through June is given by the function 
.
Is C continuous at
?
.Is C continuous at
? Question
For the function in this problem, approximate 
near 
by graphing the function on a graphing utility. Then, zoom in near the point until the graph appears straight, pick two points, and find the slope of the line you see. Round your answer to four decimal places. 
A) -0.1641
B) -0.1698
C) -0.5411
D) -0.5102
E) -0.3735
near by graphing the function on a graphing utility. Then, zoom in near the point until the graph appears straight, pick two points, and find the slope of the line you see. Round your answer to four decimal places. A) -0.1641
B) -0.1698
C) -0.5411
D) -0.5102
E) -0.3735
Question
For the function in this problem, approximate 
near the point 
by graphing the function on a graphing utility. Then, zoom in near the point until the graph appears straight, pick two points, and find the slope of the line you see. Round your answer to three decimal places. 
A) 48.050
B) -9.000
C) -8.950
D) 50.970
E) -8.999
near the point by graphing the function on a graphing utility. Then, zoom in near the point until the graph appears straight, pick two points, and find the slope of the line you see. Round your answer to three decimal places. A) 48.050
B) -9.000
C) -8.950
D) 50.970
E) -8.999
Question
The tangent line to the graph of f (x) at 
is shown. On the tangent line, P is the point of tangency and A is another point on the line. Find the instantaneous rate of change of f (x) at P. 
A) -3
B) 2
C) 1
D) -4
E) does not exist
is shown. On the tangent line, P is the point of tangency and A is another point on the line. Find the instantaneous rate of change of f (x) at P. A) -3
B) 2
C) 1
D) -4
E) does not exist
Question
For the function in this problem, approximate 
by computing 
with 
. 
A) 72.9793
B) 73.0369
C) 73.0027
D) 73.1261
E) 72.8793
by computing with . A) 72.9793
B) 73.0369
C) 73.0027
D) 73.1261
E) 72.8793
Question
The tangent line to the graph of f (x) at 
is shown. On the tangent line, P is the point of tangency and A is another point on the line. Use the coordinates of P and A to find the slope of the tangent line. 
A) 2
B) 1
C) -4
D) 5
E) does not exist
is shown. On the tangent line, P is the point of tangency and A is another point on the line. Use the coordinates of P and A to find the slope of the tangent line. A) 2
B) 1
C) -4
D) 5
E) does not exist
Question
The monthly charge in dollars for x kilowatt-hours (kWh) of electricity used by a residential consumer of Excelsior Electric Membership Corporation from November through June is given by the function 
.
Is C continuous at
?
.Is C continuous at
?
Question
For the function in this problem, find the derivative, by using the definition. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Given 
, find the average rate of change of f (x) over the following pair of intervals using a calculator if desired: 
and 
A) 17.9 and 17.99
B) 20.9 and 20.99
C) 19.90 and 19.99
D) 19.90 and 20.99
E) 17.9 and 19.99
, find the average rate of change of f (x) over the following pair of intervals using a calculator if desired: and A) 17.9 and 17.99
B) 20.9 and 20.99
C) 19.90 and 19.99
D) 19.90 and 20.99
E) 17.9 and 19.99
Question
The tangent line to the graph of f (x) at 
is shown. On the tangent line, P is the point of tangency and A is another point on the line. Find 
. 
A) 2
B) -2
C) 1
D) -5
E) does not exist
is shown. On the tangent line, P is the point of tangency and A is another point on the line. Find . A) 2
B) -2
C) 1
D) -5
E) does not exist
Question
For the function in this problem, find the slope of the tangent line at the given value. 
; 
A) 5
B) 19
C) 13
D) -1
E) 21
; A) 5
B) 19
C) 13
D) -1
E) 21
Question
Let 
. Use the definition of derivative and the Procedure/Example table in this section to verify that 
. Then, find the slope of the tangent to the graph of 
at 
.
A) 27
B) 12
C) -27
D) -12
E) 0
. Use the definition of derivative and the Procedure/Example table in this section to verify that . Then, find the slope of the tangent to the graph of at . A) 27
B) 12
C) -27
D) -12
E) 0
Question
Let 
. Use the definition of derivative and the Procedure/Example table in this section to verify that 
. Then, find the instantaneous rate of change of f (x) at 
.
A) 10
B) 2
C) 8
D) 4
E) -8
. Use the definition of derivative and the Procedure/Example table in this section to verify that . Then, find the instantaneous rate of change of f (x) at . A) 10
B) 2
C) 8
D) 4
E) -8
Question
For the function in this problem, approximate 
by using the numerical derivative feature of a graphing utility. 
A) 93
B) 75
C) 19
D) -51
E) 84
by using the numerical derivative feature of a graphing utility. A) 93
B) 75
C) 19
D) -51
E) 84
Question
For the function in this problem, approximate 
by computing 
with 
. 
A) -0.0171
B) 0.2730
C) -1.0325
D) -0.0483
E) 0.0537
by computing with . A) -0.0171
B) 0.2730
C) -1.0325
D) -0.0483
E) 0.0537
Question
The percent p of particulate pollution that can be removed from the smokestacks of an industrial plant by spending C dollars is given by 
. Find the percent of the pollution that could be removed if spending C were allowed to increase without bound.
A) 1,700%
B) 17,000%
C) 0%
D) 200%
E) 100%
. Find the percent of the pollution that could be removed if spending C were allowed to increase without bound. A) 1,700%
B) 17,000%
C) 0%
D) 200%
E) 100%
Question
The monthly charge in dollars for x kilowatt-hours (kWh) of electricity used by a residential consumer of Excelsior Electric Membership Corporation from November through June is given by the function 
. What is the monthly charge if 1,700 kWh of electricity is consumed in a month? Round your answer to two decimal places.
A) $1,700.00
B) $169.80
C) $141.30
D) $73.80
E) $118.80
. What is the monthly charge if 1,700 kWh of electricity is consumed in a month? Round your answer to two decimal places.A) $1,700.00
B) $169.80
C) $141.30
D) $73.80
E) $118.80
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Deck 9: Derivatives
1
Use the graph of and the given c-value to find .
A) 4
B) 0
C) 2
D) -6
E) does not exist
and the given c-value to find . A) 4
B) 0
C) 2
D) -6
E) does not exist
does not exist
2
A graph of is shown and a c-value is given. For this problem, use the graph to find .
A) 5
B) -15
C) 0
D) 15
E) does not exist
is shown and a c-value is given. For this problem, use the graph to find . A) 5
B) -15
C) 0
D) 15
E) does not exist
15
3
A graph of is shown and a c-value is given. For this problem, use the graph to find .
A) 0
B) 5
C) -5
D) -6
E) does not exist
is shown and a c-value is given. For this problem, use the graph to find . A) 0
B) 5
C) -5
D) -6
E) does not exist
0
4
A graph of is shown and a c-value is given. For this problem, use the graph to find .
A) 0
B) 2
C) -4
D) -6
E) does not exist
is shown and a c-value is given. For this problem, use the graph to find . A) 0
B) 2
C) -4
D) -6
E) does not exist
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5
Use the graph of and the given c-value to find .
A) 2
B) -2
C) 6
D) 0
E) does not exist
and the given c-value to find . A) 2
B) -2
C) 6
D) 0
E) does not exist
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6
Use properties of limits and algebraic methods to find the limit, if it exists.
A) -45
B) 54
C) 45
D) -54
E) does not exist
A) -45
B) 54
C) 45
D) -54
E) does not exist
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7
Complete the table and use it to predict the limit, if it exists.
A) -5
B) 5
C) -4
D) 4
E) does not exist
A) -5
B) 5
C) -4
D) 4
E) does not exist
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8
A graph of is shown and a c-value is given. For this problem, use the graph to find .
A) 5
B) 0
C) -15
D) 15
E) does not exist
is shown and a c-value is given. For this problem, use the graph to find . A) 5
B) 0
C) -15
D) 15
E) does not exist
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9
Use properties of limits and algebraic methods to find if the limit exists.
A) 0
B) 10
C) ∞
D) -10
E) 5
if the limit exists. A) 0
B) 10
C) ∞
D) -10
E) 5
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10
Use the graph of and the given c-value to find .
A) -8
B) -6
C) 3
D) -4
E) does not exist
and the given c-value to find . A) -8
B) -6
C) 3
D) -4
E) does not exist
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11
Use the graph of and the given c-value to find .
A) -6
B) 0
C) 8
D) 2
E) does not exist
and the given c-value to find . A) -6
B) 0
C) 8
D) 2
E) does not exist
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12
Complete the table and use it to predict the limit, if it exists.
A) 44.0
B) -22.0
C) 22.0
D) -0.5
E) does not exist
A) 44.0
B) -22.0
C) 22.0
D) -0.5
E) does not exist
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13
Use properties of limits and algebraic methods to find the limit, if it exists.
A) 63
B) 65
C) 60
D) 68
E) does not exist
A) 63
B) 65
C) 60
D) 68
E) does not exist
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14
Use the graph of and the given c-value to find .
A) -6
B) 0
C) 2
D) 6
E) does not exist
and the given c-value to find . A) -6
B) 0
C) 2
D) 6
E) does not exist
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15
Use properties of limits and algebraic methods to find the limit, if it exists.
A)
B)
C)
D)
E) does not exist
A)
B)
C)
D)
E) does not exist
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k this deck
16
Use properties of limits and algebraic methods to find the limit, if it exists.
A)
B)
C)
D)
E) does not exist
A)
B)
C)
D)
E) does not exist
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k this deck
17
Use the graph of and the given c-value to find .
A) -6
B) -5
C) -1
D) 3
E) does not exist
and the given c-value to find . A) -6
B) -5
C) -1
D) 3
E) does not exist
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k this deck
18
Use properties of limits and algebraic methods to find the limit, if it exists.
A)
B) -3
C)
D)
E) does not exist
A)
B) -3
C)
D)
E) does not exist
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k this deck
19
Use the graph of and the given c-value to find .
A) -6
B) -9
C) -1
D) 3
E) does not exist
and the given c-value to find . A) -6
B) -9
C) -1
D) 3
E) does not exist
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k this deck
20
Use the graph of and the given c-value to find .
A) -6
B) -7
C) 3
D) -5
E) does not exist
and the given c-value to find . A) -6
B) -7
C) 3
D) -5
E) does not exist
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k this deck
21
If and , find .
A)
B)
C) -10
D)
E) does not exist
and , find . A)
B)
C) -10
D)
E) does not exist
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k this deck
22
Determine whether the function is continuous or discontinuous at the given x-value.
A) continuous
B) discontinuous
A) continuous
B) discontinuous
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23
For the given x-value, use the figure to determine whether the function is continuous or discontinuous at that x-value.
A) discontinuous
B) continuous
A) discontinuous
B) continuous
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24
If and , find .
A) 20
B) 6
C) -2
D) -14
E) does not exist
and , find . A) 20
B) 6
C) -2
D) -14
E) does not exist
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k this deck
25
Determine whether the given function is continuous. If it is not, identify where it is discontinuous.
A) discontinuous at
B) discontinuous at
C) discontinuous at
D) discontinuous at
E) continuous everywhere
A) discontinuous at
B) discontinuous at
C) discontinuous at
D) discontinuous at
E) continuous everywhere
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26
Use properties of limits and algebraic methods to find the limit, if it exists.
A) 0
B) -2
C) 2
D) 7
E) does not exist
A) 0
B) -2
C) 2
D) 7
E) does not exist
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27
Suppose that the cost C in dollars of obtaining water that contains p percent impurities is given by . Find , if it exists.
A) $0
B) $13
C) $117
D) $1,300
E) does not exist
. Find , if it exists. A) $0
B) $13
C) $117
D) $1,300
E) does not exist
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28
A certain calling card costs 6.1 cents per minute to make a call, rounded up to the nearest minute. However, when the card is used at a pay phone, there is an additional 61 cent connection fee. If is the charge from a pay phone for a call lasting t minutes, create a table of charges for calls lasting close to 1 minute and use it to find the following limit, if it exists. Round your answer to the nearest cent.
A) $0
B) $0.61
C) $0.73
D) $0.67
E) does not exist
is the charge from a pay phone for a call lasting t minutes, create a table of charges for calls lasting close to 1 minute and use it to find the following limit, if it exists. Round your answer to the nearest cent. A) $0
B) $0.61
C) $0.73
D) $0.67
E) does not exist
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29
Use properties of limits and algebraic methods to find the limit, if it exists.
A) 0
B)
C)
D)
E) does not exist
A) 0
B)
C)
D)
E) does not exist
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k this deck
30
A certain calling card costs 5.2 cents per minute to make a call, rounded up to the nearest minute. However, when the card is used at a pay phone, there is an additional 52 cent connection fee. If is the charge from a pay phone for a call lasting t minutes, create a table of charges for calls lasting close to 1 minute and use it to find the following limit, if it exists. Round your answer to the nearest cent.
A) $0
B) $0.45
C) $0.57
D) $0.44
E) does not exist
is the charge from a pay phone for a call lasting t minutes, create a table of charges for calls lasting close to 1 minute and use it to find the following limit, if it exists. Round your answer to the nearest cent. A) $0
B) $0.45
C) $0.57
D) $0.44
E) does not exist
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k this deck
31
Graph the function with a graphing utility and use it to predict the limit. Check your work either by using the table feature of the graphing utility or by finding the limit algebraically.
A)
B) 18
C)
D) 0
E) does not exist
A)
B) 18
C)
D) 0
E) does not exist
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k this deck
32
Graph the function with a graphing utility and use it to predict the limit. Check your work either by using the table feature of the graphing utility or by finding the limit algebraically.
A) 10
B) 3
C)
D) 0
E) does not exist
A) 10
B) 3
C)
D) 0
E) does not exist
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33
If and , find .
A) -106
B) -96
C) -81
D) 0
E) does not exist
and , find . A) -106
B) -96
C) -81
D) 0
E) does not exist
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k this deck
34
A certain calling card costs 6.8 cents per minute to make a call, rounded up to the nearest minute. However, when the card is used at a pay phone, there is an additional 68 cent connection fee. If is the charge from a pay phone for a call lasting t minutes, create a table of charges for calls lasting close to 1 minute and use it to find the following limit, if it exists. Round your answer to the nearest cent.
A) $0
B) $0.68
C) $0.75
D) $0.82
E) does not exist
is the charge from a pay phone for a call lasting t minutes, create a table of charges for calls lasting close to 1 minute and use it to find the following limit, if it exists. Round your answer to the nearest cent. A) $0
B) $0.68
C) $0.75
D) $0.82
E) does not exist
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k this deck
35
Suppose that the cost C in dollars of obtaining water that contains p percent impurities is given by . Find , if it exists.
A) $0
B) $20
C) $200
D) $2,000
E) does not exist
. Find , if it exists. A) $0
B) $20
C) $200
D) $2,000
E) does not exist
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36
Determine whether the function is continuous or discontinuous at the given x-value.
A) discontinuous
B) continuous
A) discontinuous
B) continuous
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k this deck
37
If the revenue for a product (in dollars) is , and the average revenue per unit is , , find .
A) $900 per unit
B) $0.7 per unit
C) $90 per unit
D) $0 per unit
E) does not exist
, and the average revenue per unit is , , find . A) $900 per unit
B) $0.7 per unit
C) $90 per unit
D) $0 per unit
E) does not exist
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k this deck
38
Graph the function with a graphing utility and use it to predict the limit. Check your work either by using the table feature of the graphing utility or by finding the limit algebraically.
A) 0
B) 9
C)
D)
E) does not exist
A) 0
B) 9
C)
D)
E) does not exist
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k this deck
39
If the revenue for a product (in dollars) is and the average revenue per unit is , , find .
A) $520 per unit
B) $545 per unit
C) $530 per unit
D) $0 per unit
E) does not exist
and the average revenue per unit is , , find . A) $520 per unit
B) $545 per unit
C) $530 per unit
D) $0 per unit
E) does not exist
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40
If the profit function for a product is given by , find .
A) -3,600
B) -1,600
C) -2,725
D) -4,100
E) does not exist
, find . A) -3,600
B) -1,600
C) -2,725
D) -4,100
E) does not exist
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41
Suppose that the cost C of removing p percent of the particulate pollution from the exhaust gases at an industrial site is given by . Describe any discontinuities for C(p). Explain what each discontinuity means.
A) C(p) is discontinuous at . This means that not all pollution can be removed.
B) C(p) is discontinuous at . This means that none of the pollution can be removed.
C) C(p) is continuous everywhere.
D) C(p) is discontinuous at . This means that not all pollution can be removed.
E) C(p) is discontinuous at . This means that none of the pollution can be removed.
. Describe any discontinuities for C(p). Explain what each discontinuity means. A) C(p) is discontinuous at
. This means that not all pollution can be removed.B) C(p) is discontinuous at
. This means that none of the pollution can be removed.C) C(p) is continuous everywhere.
D) C(p) is discontinuous at
. This means that not all pollution can be removed.E) C(p) is discontinuous at
. This means that none of the pollution can be removed. Unlock Deck
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k this deck
42
Use analytic methods to evaluate the limit and determine which type of asymptote (if any) it represents. You can verify your conclusion by graphing the function with a graphing utility, if one is available.
A) limit = 10, horizontal asymptote
B) limit = 10, vertical asymptote
C) limit = 4, horizontal asymptote
D) limit = 4, vertical asymptote
E) does not exist, no asymptote
A) limit = 10, horizontal asymptote
B) limit = 10, vertical asymptote
C) limit = 4, horizontal asymptote
D) limit = 4, vertical asymptote
E) does not exist, no asymptote
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43
Suppose that the average number of minutes M that it takes a new employee to assemble one unit of a product is given by , where t is the number of days on the job. Is this function continuous for all
, where t is the number of days on the job. Is this function continuous for all Unlock Deck
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44
Graph the function using a window with and . What does the graph indicate about
A) -5
B) 5
C) 30
D) 0
E) does not exist
and . What does the graph indicate about A) -5
B) 5
C) 30
D) 0
E) does not exist
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k this deck
45
Use analytic methods to find the limit as for the given function.
A) -1500
B) 1500
C) -620
D) 620
E) does not exist
for the given function. A) -1500
B) 1500
C) -620
D) 620
E) does not exist
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k this deck
46
Suppose that the average number of minutes M that it takes a new employee to assemble one unit of a product is given by , where t is the number of days on the job. What is the domain for this application?
A)
B)
C)
D)
E)
, where t is the number of days on the job. What is the domain for this application? A)
B)
C)
D)
E)
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47
Determine whether the given function is continuous. If it is not, identify where it is discontinuous and which condition fails to hold. You can verify your conclusions by graphing the function with a graphing utility, if one is available.
A) discontinuous at
B) discontinuous at
C) discontinuous at
D) discontinuous at
E) continuous everywhere
A) discontinuous at
B) discontinuous at
C) discontinuous at
D) discontinuous at
E) continuous everywhere
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k this deck
48
This problem contains a function and its graph, where . Use the graph to determine, as well as you can, . Check your conclusion by using the function to determine analytically.
A) 3
B) 0
C) 4
D) 1
E) does not exist
. Use the graph to determine, as well as you can, . Check your conclusion by using the function to determine analytically. A) 3
B) 0
C) 4
D) 1
E) does not exist
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k this deck
49
This problem contains a function and its graph, where . Use the graph to determine, as well as you can, the vertical asymptote. Check your conclusion by using the function to determine the vertical asymptote analytically.
A)
B)
C)
D)
E) no vertical asymptote
. Use the graph to determine, as well as you can, the vertical asymptote. Check your conclusion by using the function to determine the vertical asymptote analytically. A)
B)
C)
D)
E) no vertical asymptote
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50
Determine whether the given function is continuous. If it is not, identify where it is discontinuous. You can verify your conclusions by graphing the function with a graphing utility, if one is available.
A) discontinuous at
B) discontinuous at
C) discontinuous at
D) discontinuous at
E) continuous everywhere
A) discontinuous at
B) discontinuous at
C) discontinuous at
D) discontinuous at
E) continuous everywhere
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51
This problem contains a function and its graph, where . Use the graph to determine, as well as you can, the horizontal asymptote. Check your conclusion by using the function to determine the horizontal asymptote analytically.
A)
B)
C)
D)
E)
. Use the graph to determine, as well as you can, the horizontal asymptote. Check your conclusion by using the function to determine the horizontal asymptote analytically. A)
B)
C)
D)
E)
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52
Use analytic methods to find the limit as for the given function.
A) 920
B) 240
C) -920
D) -240
E) does not exist
for the given function. A) 920
B) 240
C) -920
D) -240
E) does not exist
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k this deck
53
Use analytic methods to find any point of discontinuity for the given function.
A)
B)
C)
D)
E) continuous everywhere
A)
B)
C)
D)
E) continuous everywhere
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54
Suppose that the average number of minutes M that it takes a new employee to assemble one unit of a product is given by , where t is the number of days on the job. Is this function continuous for all values of t?
, where t is the number of days on the job. Is this function continuous for all values of t? Unlock Deck
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k this deck
55
Determine whether the given function is continuous. If is not continuous, identify where it is discontinuous and which condition(s) fails to hold.
A) is discontinuous at since is not defined and does not exist.
B) is discontinuous at since is not defined and does not exist.
C) is discontinuous at since is not defined and does not exist.
D) is continuous.
E) is discontinuous at since is not defined and does not exist.
is continuous. If is not continuous, identify where it is discontinuous and which condition(s) fails to hold. A)
is discontinuous at since is not defined and does not exist.B)
is discontinuous at since is not defined and does not exist.C)
is discontinuous at since is not defined and does not exist.D)
is continuous.E)
is discontinuous at since is not defined and does not exist. Unlock Deck
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56
Use a table utility with x-values larger than 10,000 to investigate . What does the table indicate about ?
A) -3
B) 3
C) 6
D) 0
E) does not exist
. What does the table indicate about ? A) -3
B) 3
C) 6
D) 0
E) does not exist
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57
This problem contains a function and its graph, where . Use the graph to determine, as well as you can, . Check your conclusion by using the function to determine analytically.
A) 4
B) 1
C) 3
D) 0
E) does not exist
. Use the graph to determine, as well as you can, . Check your conclusion by using the function to determine analytically. A) 4
B) 1
C) 3
D) 0
E) does not exist
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k this deck
58
Use analytic methods to evaluate the limit and determine which type of asymptote (if any) it represents. You can verify your conclusion by graphing the function with a graphing utility, if one is available.
A) limit = 0, vertical asymptote
B) limit = 0, horizontal asymptote
C) limit = 2, horizontal asymptote
D) limit = 2, vertical asymptote
E) does not exist
A) limit = 0, vertical asymptote
B) limit = 0, horizontal asymptote
C) limit = 2, horizontal asymptote
D) limit = 2, vertical asymptote
E) does not exist
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59
Use analytic methods to evaluate the limit and determine which type of asymptote (if any) it represents. You can verify your conclusion by graphing the function with a graphing utility, if one is available.
A) limit = 4, vertical asymptote
B) limit = 8, horizontal asymptote
C) limit = 8, vertical asymptote
D) limit = 4, horizontal asymptote
E) does not exist
A) limit = 4, vertical asymptote
B) limit = 8, horizontal asymptote
C) limit = 8, vertical asymptote
D) limit = 4, horizontal asymptote
E) does not exist
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60
Suppose that the average number of minutes M that it takes a new employee to assemble one unit of a product is given by , where t is the number of days on the job. Is this function continuous at
, where t is the number of days on the job. Is this function continuous at Unlock Deck
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61
For the function in this problem, approximate by using the numerical derivative feature of a graphing utility. Round your answer to three decimal places.
A) -0.298
B) -0.421
C) -0.544
D) -0.187
E) -0.655
by using the numerical derivative feature of a graphing utility. Round your answer to three decimal places. A) -0.298
B) -0.421
C) -0.544
D) -0.187
E) -0.655
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62
For the given function, find the average rate of change over the specified interval. over
A) 0
B) 4
C) 2
D) -17
E) 17
over A) 0
B) 4
C) 2
D) -17
E) 17
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63
For the function in this problem, find the instantaneous rate of change of the function at the given value. ;
A) 18
B) 6
C) 10
D) 14
E) 13
; A) 18
B) 6
C) 10
D) 14
E) 13
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64
The monthly charge in dollars for x kilowatt-hours (kWh) of electricity used by a residential consumer of Excelsior Electric Membership Corporation from November through June is given by the function .
Is C continuous at ?
.Is C continuous at
? Unlock Deck
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65
For the function in this problem, approximate near by graphing the function on a graphing utility. Then, zoom in near the point until the graph appears straight, pick two points, and find the slope of the line you see. Round your answer to four decimal places.
A) -0.1641
B) -0.1698
C) -0.5411
D) -0.5102
E) -0.3735
near by graphing the function on a graphing utility. Then, zoom in near the point until the graph appears straight, pick two points, and find the slope of the line you see. Round your answer to four decimal places. A) -0.1641
B) -0.1698
C) -0.5411
D) -0.5102
E) -0.3735
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66
For the function in this problem, approximate near the point by graphing the function on a graphing utility. Then, zoom in near the point until the graph appears straight, pick two points, and find the slope of the line you see. Round your answer to three decimal places.
A) 48.050
B) -9.000
C) -8.950
D) 50.970
E) -8.999
near the point by graphing the function on a graphing utility. Then, zoom in near the point until the graph appears straight, pick two points, and find the slope of the line you see. Round your answer to three decimal places. A) 48.050
B) -9.000
C) -8.950
D) 50.970
E) -8.999
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Unlock Deck
k this deck
67
The tangent line to the graph of f (x) at is shown. On the tangent line, P is the point of tangency and A is another point on the line. Find the instantaneous rate of change of f (x) at P.
A) -3
B) 2
C) 1
D) -4
E) does not exist
is shown. On the tangent line, P is the point of tangency and A is another point on the line. Find the instantaneous rate of change of f (x) at P. A) -3
B) 2
C) 1
D) -4
E) does not exist
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Unlock Deck
k this deck
68
For the function in this problem, approximate by computing with .
A) 72.9793
B) 73.0369
C) 73.0027
D) 73.1261
E) 72.8793
by computing with . A) 72.9793
B) 73.0369
C) 73.0027
D) 73.1261
E) 72.8793
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Unlock Deck
k this deck
69
The tangent line to the graph of f (x) at is shown. On the tangent line, P is the point of tangency and A is another point on the line. Use the coordinates of P and A to find the slope of the tangent line.
A) 2
B) 1
C) -4
D) 5
E) does not exist
is shown. On the tangent line, P is the point of tangency and A is another point on the line. Use the coordinates of P and A to find the slope of the tangent line. A) 2
B) 1
C) -4
D) 5
E) does not exist
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k this deck
70
The monthly charge in dollars for x kilowatt-hours (kWh) of electricity used by a residential consumer of Excelsior Electric Membership Corporation from November through June is given by the function .
Is C continuous at ?
.Is C continuous at
?
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Unlock Deck
k this deck
71
For the function in this problem, find the derivative, by using the definition.
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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k this deck
72
Given , find the average rate of change of f (x) over the following pair of intervals using a calculator if desired: and
A) 17.9 and 17.99
B) 20.9 and 20.99
C) 19.90 and 19.99
D) 19.90 and 20.99
E) 17.9 and 19.99
, find the average rate of change of f (x) over the following pair of intervals using a calculator if desired: and A) 17.9 and 17.99
B) 20.9 and 20.99
C) 19.90 and 19.99
D) 19.90 and 20.99
E) 17.9 and 19.99
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73
The tangent line to the graph of f (x) at is shown. On the tangent line, P is the point of tangency and A is another point on the line. Find .
A) 2
B) -2
C) 1
D) -5
E) does not exist
is shown. On the tangent line, P is the point of tangency and A is another point on the line. Find . A) 2
B) -2
C) 1
D) -5
E) does not exist
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74
For the function in this problem, find the slope of the tangent line at the given value. ;
A) 5
B) 19
C) 13
D) -1
E) 21
; A) 5
B) 19
C) 13
D) -1
E) 21
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75
Let . Use the definition of derivative and the Procedure/Example table in this section to verify that . Then, find the slope of the tangent to the graph of at .
A) 27
B) 12
C) -27
D) -12
E) 0
. Use the definition of derivative and the Procedure/Example table in this section to verify that . Then, find the slope of the tangent to the graph of at . A) 27
B) 12
C) -27
D) -12
E) 0
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76
Let . Use the definition of derivative and the Procedure/Example table in this section to verify that . Then, find the instantaneous rate of change of f (x) at .
A) 10
B) 2
C) 8
D) 4
E) -8
. Use the definition of derivative and the Procedure/Example table in this section to verify that . Then, find the instantaneous rate of change of f (x) at . A) 10
B) 2
C) 8
D) 4
E) -8
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k this deck
77
For the function in this problem, approximate by using the numerical derivative feature of a graphing utility.
A) 93
B) 75
C) 19
D) -51
E) 84
by using the numerical derivative feature of a graphing utility. A) 93
B) 75
C) 19
D) -51
E) 84
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78
For the function in this problem, approximate by computing with .
A) -0.0171
B) 0.2730
C) -1.0325
D) -0.0483
E) 0.0537
by computing with . A) -0.0171
B) 0.2730
C) -1.0325
D) -0.0483
E) 0.0537
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k this deck
79
The percent p of particulate pollution that can be removed from the smokestacks of an industrial plant by spending C dollars is given by . Find the percent of the pollution that could be removed if spending C were allowed to increase without bound.
A) 1,700%
B) 17,000%
C) 0%
D) 200%
E) 100%
. Find the percent of the pollution that could be removed if spending C were allowed to increase without bound. A) 1,700%
B) 17,000%
C) 0%
D) 200%
E) 100%
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Unlock Deck
k this deck
80
The monthly charge in dollars for x kilowatt-hours (kWh) of electricity used by a residential consumer of Excelsior Electric Membership Corporation from November through June is given by the function . What is the monthly charge if 1,700 kWh of electricity is consumed in a month? Round your answer to two decimal places.
A) $1,700.00
B) $169.80
C) $141.30
D) $73.80
E) $118.80
. What is the monthly charge if 1,700 kWh of electricity is consumed in a month? Round your answer to two decimal places.A) $1,700.00
B) $169.80
C) $141.30
D) $73.80
E) $118.80
Unlock Deck
Unlock for access to all 250 flashcards in this deck.
Unlock Deck
k this deck
Unlock Deck
Unlock for access to all 250 flashcards in this deck.
