تكلم مع الذكاء الاصطناعي
Deck 10: Derivatives
ملء الشاشة (f)
سؤال
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
سؤال
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
سؤال
Use properties of limits and algebraic methods to find the limit, if it exists. 
A)97
B)99
C)94
D)102
E)does not exist
A)97
B)99
C)94
D)102
E)does not exist
سؤال
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
سؤال
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
سؤال
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
سؤال
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
سؤال
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
سؤال
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
سؤال
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
سؤال
A graph of 
is shown and a c-value is given. For this problem, use the graph to find 
. 
A)10
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)10
B)-15
C)0
D)15
E)does not exist
سؤال
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
سؤال
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
سؤال
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
سؤال
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
سؤال
Use the graph of 
and the given c-value to find 
. 
A)-6
B)-1
C)3
D)does not exist
and the given c-value to find . A)-6
B)-1
C)3
D)does not exist
سؤال
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
سؤال
Use the graph of 
and the given c-value to find 
. 
A)
B)-8
C)3
D)-1
E)does not exist
and the given c-value to find . A)
B)-8
C)3
D)-1
E)does not exist
سؤال
A graph of 
is shown and a c-value is given. For this problem, use the graph to find 
. 
A)0
B)2
C)-6
D)-4
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)-6
D)-4
E)does not exist
سؤال
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
سؤال
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
سؤال
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
سؤال
If 
and 
, find 
.
A)
B)
C)-10
D)
E)does not exist
and , find . A)
B)
C)-10
D)
E)does not exist
سؤال
Determine whether the function is continuous or discontinuous at the given x-value. 
A)continuous
B)discontinuous
A)continuous
B)discontinuous
سؤال
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
سؤال
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
سؤال
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
سؤال
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)18
B)4
C)
D)0
E)does not exist
A)18
B)4
C)
D)0
E)does not exist
سؤال
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
سؤال
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
سؤال
A certain calling card costs 6.3 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 63 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)$0.56
C)$0.69
D)$0.78
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)$0.56
C)$0.69
D)$0.78
E)does not exist
سؤال
Determine whether the function is continuous or discontinuous at the given x-value. 
A)continuous
B)discontinuous
A)continuous
B)discontinuous
سؤال
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
سؤال
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
سؤال
If the revenue for a product (in dollars) is 
, and the average revenue per unit is 
, 
, find 
.
A)$500 per unit
B)$0.8 per unit
C)$50 per unit
D)$0 per unit
E)does not exist
, and the average revenue per unit is , , find . A)$500 per unit
B)$0.8 per unit
C)$50 per unit
D)$0 per unit
E)does not exist
سؤال
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
سؤال
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
سؤال
If 
and 
, find 
.
A)-95
B)-85
C)-70
D)0
E)does not exist
and , find . A)-95
B)-85
C)-70
D)0
E)does not exist
سؤال
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
سؤال
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
سؤال
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
سؤال
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 
A)Yes
B)No
, where t is the number of days on the job. Is this function continuous for all A)Yes
B)No
سؤال
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.
سؤال
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 = 3, vertical asymptote
B)limit = 6, horizontal asymptote
C)limit = 6, vertical asymptote
D)limit = 3, horizontal asymptote
E)does not exist
A)limit = 3, vertical asymptote
B)limit = 6, horizontal asymptote
C)limit = 6, vertical asymptote
D)limit = 3, horizontal asymptote
E)does not exist
سؤال
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
سؤال
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
سؤال
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.
سؤال
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
سؤال
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
سؤال
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
سؤال
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
سؤال
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)
سؤال
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
سؤال
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?
A)Yes
B)No
, where t is the number of days on the job. Is this function continuous for all values of t?A)Yes
B)No
سؤال
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
سؤال
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
سؤال
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 
A)Yes
B)No
, where t is the number of days on the job. Is this function continuous at A)Yes
B)No
سؤال
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
سؤال
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
سؤال
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)
سؤال
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)-0.0835
B)-0.0813
C)-0.0352
D)-0.0358
E)-0.0517
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)-0.0835
B)-0.0813
C)-0.0352
D)-0.0358
E)-0.0517
سؤال
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
سؤال
For the function in this problem, find the instantaneous rate of change of the function at the given value. 
; 
A)28
B)8
C)16
D)20
E)45
; A)28
B)8
C)16
D)20
E)45
سؤال
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 1,100 kWh of electricity is consumed in a month? Round your answer to two decimal places.
A)$1,100
B)$113.40
C)$96.30
D)$81.30
E)$91.30
.
What is the monthly charge if 1,100 kWh of electricity is consumed in a month? Round your answer to two decimal places.
A)$1,100
B)$113.40
C)$96.30
D)$81.30
E)$91.30
سؤال
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
سؤال
The tangent line to the graph of 
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 
at P. 
A)-3
B)3
C)-4
D)-5
E)does not exist
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 at P. A)-3
B)3
C)-4
D)-5
E)does not exist
سؤال
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%
سؤال
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
سؤال
For the function in this problem, find the derivative, by using the definition. 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
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
سؤال
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
سؤال
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
سؤال
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)53
B)23
C)-53
D)-23
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)53
B)23
C)-53
D)-23
E)0
سؤال
For the function in this problem, approximate 
by computing 
with 
. Round your answer to four decimal places. 
A)30.9784
B)31.0360
C)31.0018
D)31.1252
E)30.8784
by computing with . Round your answer to four decimal places. A)30.9784
B)31.0360
C)31.0018
D)31.1252
E)30.8784
سؤال
For the given function, find the average rate of change over the specified interval. 
over 
A)0
B)-2
C)6
D)-34
E)34
over A)0
B)-2
C)6
D)-34
E)34
سؤال
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
سؤال
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 
?
A)Yes
B)No
. Is C continuous at ?
A)Yes
B)No
سؤال
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 
?
A)Yes
B)No
. Is C continuous at ?A)Yes
B)No
سؤال
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
سؤال
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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العب
ملء الشاشة (f)
Deck 10: Derivatives
1
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
does not exist
2
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
-3
3
Use properties of limits and algebraic methods to find the limit, if it exists.
A)97
B)99
C)94
D)102
E)does not exist
A)97
B)99
C)94
D)102
E)does not exist
99
4
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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5
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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6
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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7
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
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8
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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9
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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10
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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11
A graph of is shown and a c-value is given. For this problem, use the graph to find .
A)10
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)10
B)-15
C)0
D)15
E)does not exist
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12
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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13
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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14
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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15
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
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16
Use the graph of and the given c-value to find .
A)-6
B)-1
C)3
D)does not exist
and the given c-value to find . A)-6
B)-1
C)3
D)does not exist
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17
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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18
Use the graph of and the given c-value to find .
A)
B)-8
C)3
D)-1
E)does not exist
and the given c-value to find . A)
B)-8
C)3
D)-1
E)does not exist
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19
A graph of is shown and a c-value is given. For this problem, use the graph to find .
A)0
B)2
C)-6
D)-4
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)-6
D)-4
E)does not exist
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20
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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21
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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22
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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23
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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24
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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25
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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26
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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27
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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28
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)18
B)4
C)
D)0
E)does not exist
A)18
B)4
C)
D)0
E)does not exist
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29
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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30
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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31
A certain calling card costs 6.3 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 63 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)$0.56
C)$0.69
D)$0.78
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)$0.56
C)$0.69
D)$0.78
E)does not exist
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32
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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33
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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34
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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35
If the revenue for a product (in dollars) is , and the average revenue per unit is , , find .
A)$500 per unit
B)$0.8 per unit
C)$50 per unit
D)$0 per unit
E)does not exist
, and the average revenue per unit is , , find . A)$500 per unit
B)$0.8 per unit
C)$50 per unit
D)$0 per unit
E)does not exist
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36
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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37
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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38
If and , find .
A)-95
B)-85
C)-70
D)0
E)does not exist
and , find . A)-95
B)-85
C)-70
D)0
E)does not exist
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39
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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40
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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41
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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42
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
A)Yes
B)No
, where t is the number of days on the job. Is this function continuous for all A)Yes
B)No
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43
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.
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44
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 = 3, vertical asymptote
B)limit = 6, horizontal asymptote
C)limit = 6, vertical asymptote
D)limit = 3, horizontal asymptote
E)does not exist
A)limit = 3, vertical asymptote
B)limit = 6, horizontal asymptote
C)limit = 6, vertical asymptote
D)limit = 3, horizontal asymptote
E)does not exist
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45
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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46
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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47
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.
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48
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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49
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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50
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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51
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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52
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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53
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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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?
A)Yes
B)No
, where t is the number of days on the job. Is this function continuous for all values of t?A)Yes
B)No
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55
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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56
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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57
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
A)Yes
B)No
, where t is the number of days on the job. Is this function continuous at A)Yes
B)No
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58
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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59
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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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. 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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61
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)-0.0835
B)-0.0813
C)-0.0352
D)-0.0358
E)-0.0517
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)-0.0835
B)-0.0813
C)-0.0352
D)-0.0358
E)-0.0517
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62
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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63
For the function in this problem, find the instantaneous rate of change of the function at the given value. ;
A)28
B)8
C)16
D)20
E)45
; A)28
B)8
C)16
D)20
E)45
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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 .
What is the monthly charge if 1,100 kWh of electricity is consumed in a month? Round your answer to two decimal places.
A)$1,100
B)$113.40
C)$96.30
D)$81.30
E)$91.30
.
What is the monthly charge if 1,100 kWh of electricity is consumed in a month? Round your answer to two decimal places.
A)$1,100
B)$113.40
C)$96.30
D)$81.30
E)$91.30
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65
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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66
The tangent line to the graph of 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 at P.
A)-3
B)3
C)-4
D)-5
E)does not exist
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 at P. A)-3
B)3
C)-4
D)-5
E)does not exist
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67
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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68
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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69
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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70
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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71
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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72
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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73
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)53
B)23
C)-53
D)-23
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)53
B)23
C)-53
D)-23
E)0
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74
For the function in this problem, approximate by computing with . Round your answer to four decimal places.
A)30.9784
B)31.0360
C)31.0018
D)31.1252
E)30.8784
by computing with . Round your answer to four decimal places. A)30.9784
B)31.0360
C)31.0018
D)31.1252
E)30.8784
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75
For the given function, find the average rate of change over the specified interval. over
A)0
B)-2
C)6
D)-34
E)34
over A)0
B)-2
C)6
D)-34
E)34
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76
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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77
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 ?
A)Yes
B)No
. Is C continuous at ?
A)Yes
B)No
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78
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 ?
A)Yes
B)No
. Is C continuous at ?A)Yes
B)No
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79
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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80
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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