Chat with AI
Deck 2: Limits and Their Properties
Full screen (f)
Question
For the function 
,use a graphing utility to complete the table and estimate the limit as x approaches infinity. x
100
101
102
103
104
105
106
β
A)1.0000
B)2.2500
C)3.4300
D)0.3500
E)does not exist
,use a graphing utility to complete the table and estimate the limit as x approaches infinity. x100
101
102
103
104
105
106
βA)1.0000
B)2.2500
C)3.4300
D)0.3500
E)does not exist
Question
Find the limit. β 
β
A)
B)-4
C)
D)4
E)-1
βA)
B)-4
C)
D)4
E)-1
Question
βUse the graphs of 
and 
given below to answer the following question:
β
Is
β continuous at 
? Explain why or why not.
and given below to answer the following question:β
Is
β continuous at ? Explain why or why not. Question
What is 
β? Explain your reasoning.
β? Explain your reasoning. Question
If 
β ,what is βkβ so that 
is continuous at 
?
β ,what is βkβ so that is continuous at ? Question
βFind the limit,if it exists: 
. β
A)β
B)β
C)β
D)βThe limit does not exist.
. βA)β
B)β
C)β
D)βThe limit does not exist.
Question
For the function 
,use a graphing utility to complete the table and estimate the limit as x approaches infinity. x
100
101
102
103
104
105
106
β
A)3
B)-2
C)8
D)0
E)None of the above
,use a graphing utility to complete the table and estimate the limit as x approaches infinity. x100
101
102
103
104
105
106
βA)3
B)-2
C)8
D)0
E)None of the above
Question
βEstimate the limit,if it exists: 
where 
is represented by the given graph: β 
β
A)β-2
B)β1
C)β-3
D)βThe limit does not exist.
where is represented by the given graph: β βA)β-2
B)β1
C)β-3
D)βThe limit does not exist.
Question
βHow many vertical asymptotes exist for the function 
in the open interval 
? β
A)β4
B)β1
C)β2
D)β3
in the open interval ? βA)β4
B)β1
C)β2
D)β3
Question
Evaluate the limit,if it exists:β 
. β
A)β-17
B)β-9
C)β17
D)βThe limit does not exist.
. βA)β-17
B)β-9
C)β17
D)βThe limit does not exist.
Question
Evaluate the limit,if it exists:β 
. β
A)β
B)β
C)β
D)βThe limit does not exist.
. βA)β
B)β
C)β
D)βThe limit does not exist.
Question
βFor what value of k is the function 
continuous at 
? β
A)β
B)β0
C)β
D)β
continuous at ? βA)β
B)β0
C)β
D)β
Question
βWhich of the following statements is true? β
A)β
.
B)β
does not exist.
C)β
does not exist.
D)β
.
A)β
.B)β
does not exist.C)β
does not exist.D)β
. Question
βIf 
is a continuous function on the closed interval 
,with 
and c is in the closed interval 
,then which of the following statements must be true? β
A)β
B)β
C)βThere is at least one value c such that
.
D)βThere is only one value c such that
.
is a continuous function on the closed interval ,with and c is in the closed interval ,then which of the following statements must be true? βA)β
B)β
C)βThere is at least one value c such that
.D)βThere is only one value c such that
. Question
For the function 
,use a graphing utility to complete the table and estimate the limit as x approaches infinity. x
100
101
102
103
104
105
106
β
A)1.3333
B)2.3333
C)0.7500
D)1.7500
E)-0.2500
,use a graphing utility to complete the table and estimate the limit as x approaches infinity. x100
101
102
103
104
105
106
βA)1.3333
B)2.3333
C)0.7500
D)1.7500
E)-0.2500
Question
Identify the vertical asymptotes for 
. β
A)β
,
B)β
C)β
D)β
,
. βA)β
,B)β
C)β
D)β
, Question
βEvaluate the limit,if it exists: 
. β
A)β
B)β
C)β
D)βThe limit does not exist.
. βA)β
B)β
C)β
D)βThe limit does not exist.
Question
Is 
β continuous at 
? Explain why or why not.
β continuous at ? Explain why or why not. Question
βEvaluate the limit,if it exists: 
. β
A)β
B)β
C)β
D)β
. βA)β
B)β
C)β
D)β
Question
βGiven the function 
.What value of k will make this piecewise function continuous? β
A)β
B)β
C)β
D)β
.What value of k will make this piecewise function continuous? βA)β
B)β
C)β
D)β
Question
Find the limit. β 
β
A)
B)-6
C)0
D)
E)
βA)
B)-6
C)0
D)
E)
Question
Question
Find all the vertical asymptotes (if any)of the graph of the function 
. β
A)
B)
C)
D)
E)no vertical asymptotes
. βA)
B)
C)
D)
E)no vertical asymptotes
Question
The graph shows the temperature T,in degrees Fahrenheit,of molten glass t seconds after it is removed from a kiln. β 
β
Find
.
β
A)1,515Β°
B)65Β°
C)1,450Β°
D)82Β°
E)1,385Β°
βFind
.β
A)1,515Β°
B)65Β°
C)1,450Β°
D)82Β°
E)1,385Β°
Question
Sketch the graph of the function 
using any extrema,intercepts,symmetry,and asymptotes. β
A)β
B)β
C)β
D)β
E)β
using any extrema,intercepts,symmetry,and asymptotes. βA)β
B)β
C)β
D)β
E)β
Question
Find the limit. β 
β
A)1
B)0
C)
D)
E)does not exist
βA)1
B)0
C)
D)
E)does not exist
Question
Find all the vertical asymptotes (if any)of the graph of the function 
. β
A)
B)
C)
D)
E)no vertical asymptotes
. βA)
B)
C)
D)
E)no vertical asymptotes
Question
Find the point on the graph of the function 
that is closest to the point 
. β
A)
B)
C)
D)
E)
that is closest to the point . βA)
B)
C)
D)
E)
Question
Find the limit. β 
β
A)
B)
C)1
D)3
E)
βA)
B)
C)1
D)3
E)
Question
Sketch the graph of the relation 
using any extrema,intercepts,symmetry,and asymptotes. β
A)β
B)β
C)β
D)β
E)β
using any extrema,intercepts,symmetry,and asymptotes. βA)β
B)β
C)β
D)β
E)β
Question
Find the limit. β 
β
A)
B)
C)1
D)-5
E)
βA)
B)
C)1
D)-5
E)
Question
Sketch the graph of the function 
using any extrema,intercepts,symmetry,and asymptotes. β
A)β
B)β
C)β
D)β
E)β
using any extrema,intercepts,symmetry,and asymptotes. βA)β
B)β
C)β
D)β
E)β
Question
Sketch the graph of the relation 
using any extrema,intercepts,symmetry,and asymptotes. β
A)β
B)β
C)β
D)β
E)β
using any extrema,intercepts,symmetry,and asymptotes. βA)β
B)β
C)β
D)β
E)β
Question
A heat probe is attached to the heat exchanger of a heating system.The temperature T (in degrees Celsius)is recorded t seconds after the furnace is started.A model for the data recorded for the first two minutes is given by 
.Find 
. β
A)1,499Β°
B)1,411Β°
C)50Β°
D)88Β°
E)28Β°
.Find . βA)1,499Β°
B)1,411Β°
C)50Β°
D)88Β°
E)28Β°
Question
Find all the vertical asymptotes (if any)of the graph of the function 
. β
A)
B)
C)
D)
, 
E)no vertical asymptotes
. βA)
B)
C)
D)
, E)no vertical asymptotes
Question
A container holds 6 liters of a 25% brine solution.A model for the concentration C of the mixture after adding x liters of an 0.89% brine solution to the container and then draining x liters of the well-mixed solution is given as 
.Find 
.Round your answer to two decimal places. β
A)0.67%
B)0.33%
C)0.93%
D)0.89%
E)0.25%
.Find .Round your answer to two decimal places. βA)0.67%
B)0.33%
C)0.93%
D)0.89%
E)0.25%
Question
A business has a cost of 
for producing x units.The average cost per unit is 
.Find the limit of 
as x approaches infinity. β
A)375.0
B)1
C)600
D)0
E)1.6
for producing x units.The average cost per unit is .Find the limit of as x approaches infinity. βA)375.0
B)1
C)600
D)0
E)1.6
Question
Find the point on the graph of the function 
that is closest to the point 
.Round all numerical values in your answer to four decimal places. β
A)
B)
C)
D)
E)
that is closest to the point .Round all numerical values in your answer to four decimal places. βA)
B)
C)
D)
E)
Question
Find the vertical asymptotes (if any)of the function 
. β
A)
B)
C)β
D)
E)
. βA)
B)
C)β
D)
E)
Question
Find the limit. β 
β
A)
B)1
C)0
D)
E)
βA)
B)1
C)0
D)
E)
Question
Use the graph to determine the following limits,and discuss the continuity of the function at 
. (i) 
(ii) 
(iii) 
β 
A)1,-1,does not exist,not continuous
B)1,0,does not exist,not continuous
C)0,1,does not exist,not continuous
D)-4,0,does not exist,not continuous
E)0,1,0,continuous
. (i) (ii) (iii) β A)1,-1,does not exist,not continuous
B)1,0,does not exist,not continuous
C)0,1,does not exist,not continuous
D)-4,0,does not exist,not continuous
E)0,1,0,continuous
Question
Find the limit. β 
β
A)
B)
C)4
D)-2
E)-4
βA)
B)
C)4
D)-2
E)-4
Question
A petrol car is parked 35 feet from a long warehouse (see figure).The revolving light on top of the car turns at a rate of 
revolution per second.The rate at which the light beam moves along the wall is 
ft/sec.Find the rate r when ΞΈ is 
. β 
ft
β
A)
ft/sec
B)
ft/sec
C)
ft/sec
D)
ft/sec
E)
ft/sec
revolution per second.The rate at which the light beam moves along the wall is ft/sec.Find the rate r when ΞΈ is . β ftβ
A)
ft/secB)
ft/secC)
ft/secD)
ft/secE)
ft/sec Question
Find all vertical asymptotes (if any)of the function 
. β
A)
B)
C)
D)
E)
. βA)
B)
C)
D)
E)
Question
Find the limit (if it exists). β 
β
A)
B)0
C)Limit does not exist.
D)
E)
βA)
B)0
C)Limit does not exist.
D)
E)
Question
Use the graph as shown to determine the following limits,and discuss the continuity of the function at 
. β
(i)
(ii) 
(iii) 
β 
β
A)2,2,2,not continuous
B)3,3,3,continuous
C)4,4,4,not continuous
D)3,3,3,not continuous
E)2,2,2,continuous
. β(i)
(ii) (iii) β βA)2,2,2,not continuous
B)3,3,3,continuous
C)4,4,4,not continuous
D)3,3,3,not continuous
E)2,2,2,continuous
Question
A 35-foot ladder is leaning against a house (see figure).If the base of the ladder is pulled away from the house at a rate of 2 feet per second,the top will move down the wall at a rate of 
ft/sec,where x is the distance between the base of the ladder and the house.Find the rate r when x is 28 feet. β 
ft
β
A)
ft/sec
B)
ft/sec
C)
ft/sec
D)
ft/sec
E)
ft/sec
ft/sec,where x is the distance between the base of the ladder and the house.Find the rate r when x is 28 feet. β ftβ
A)
ft/secB)
ft/secC)
ft/secD)
ft/secE)
ft/sec Question
Use the graph as shown to determine the following limits,and discuss the continuity of the function at 
. β
(i)
(ii) 
(iii) 
β 
β
A)3,3,3,continuous
B)2,2,2,not continuous
C)3,3,3,not continuous
D)-3,-3,-3,continuous
E)2,2,2,continuous
. β(i)
(ii) (iii) β βA)3,3,3,continuous
B)2,2,2,not continuous
C)3,3,3,not continuous
D)-3,-3,-3,continuous
E)2,2,2,continuous
Question
A 20-foot ladder is leaning against a house (see figure).If the base of the ladder is pulled away from the house at a rate of 2 feet per second,the top will move down the wall at a rate of 
ft/sec,where x is the distance between the base of the ladder and the house.Find the limit of r as 
. β 
ft
β
A)
B)40
C)0
D)
E)20
ft/sec,where x is the distance between the base of the ladder and the house.Find the limit of r as . β ftβ
A)
B)40
C)0
D)
E)20
Question
Find the limit (if it exists). β 
,where 
β
A)Limit does not exist.
B)0
C)5
D)6
E)15
,where βA)Limit does not exist.
B)0
C)5
D)6
E)15
Question
Use a graphing utility to graph the function 
and determine the following one-sided limit. β 
β
A)
B)4
C)-4
D)
E)0
and determine the following one-sided limit. β βA)
B)4
C)-4
D)
E)0
Question
Find the limit (if it exists).Note that 
represents the greatest integer function. β 
β
A)3
B)-2
C)2
D)-3
E)does not exist
represents the greatest integer function. β βA)3
B)-2
C)2
D)-3
E)does not exist
Question
Find the limit. β 
β
A)1
B)0
C)-1
D)
E)
βA)1
B)0
C)-1
D)
E)
Question
Find the following limit if it exists: 
.Use 
when appropriate. β
A)
B)4
C)1
D)
E)does not exist
.Use when appropriate. βA)
B)4
C)1
D)
E)does not exist
Question
Use a graphing utility to graph the function 
and determine the one-sided limit 
. β
A)
B)
C)0
D)3
E)2
and determine the one-sided limit . βA)
B)
C)0
D)3
E)2
Question
Find the vertical asymptotes (if any)of the function 
. β
A)
B)
C)
D)
E)no vertical asymptotes
. βA)
B)
C)
D)
E)no vertical asymptotes
Question
Find the limit (if it exists). β 
β
A)0
B)
C)
D)
E)Limit does not exist.
βA)0
B)
C)
D)
E)Limit does not exist.
Question
A petrol car is parked 65 feet from a long warehouse (see figure).The revolving light on top of the car turns at a rate of 
revolution per second.The rate at which the light beam moves along the wall is 
ft/sec.Find the limit of r as 
. ββ 
β 
β ft
β
A)
B)
C)0
D)65
E)
revolution per second.The rate at which the light beam moves along the wall is ft/sec.Find the limit of r as . ββ β β ftβ
A)
B)
C)0
D)65
E)
Question
Find the limit. β 
β
A)1
B)
C)0
D)
E)β-1
βA)1
B)
C)0
D)
E)β-1
Question
Find the limit (if it exists). β 
β
A)
B)
C)0
D)
E)Limit does not exist.
βA)
B)
C)0
D)
E)Limit does not exist.
Question
Find the value of c guaranteed by the Intermediate Value Theorem. β 
, 
, 
β
A)0
B)2
C)4
D)1
E)3
, , βA)0
B)2
C)4
D)1
E)3
Question
Find the x-values (if any)at which the function 
is not continuous.Which of the discontinuities are removable? β
A)no points of discontinuity
B)
(not removable), 
(removable)
C)
(removable), 
(not removable)
D)no points of continuity
E)
(not removable), 
(not removable)
is not continuous.Which of the discontinuities are removable? βA)no points of discontinuity
B)
(not removable), (removable)C)
(removable), (not removable)D)no points of continuity
E)
(not removable), (not removable) Question
Find the value of c guaranteed by the Intermediate Value Theorem. β 
, 
, 
β
A)13
B)4
C)3
D)11
E)12
, , βA)13
B)4
C)3
D)11
E)12
Question
Find the limit. β 
β
A)
B)
C)
D)
E)does not exist
βA)
B)
C)
D)
E)does not exist
Question
Find the constant a such that the function β 
β
Is continuous on the entire real line.
β
A)
, 
B)
, 
C)
, 
D)
, 
E)
, 
βIs continuous on the entire real line.
β
A)
, B)
, C)
, D)
, E)
, Question
A long distance phone service charges $0.45 for the first 11 minutes and $0.1 for each additional minute or fraction thereof.Use the greatest integer function to write the cost C of a call in terms of time t (in minutes). β
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Question
Discuss the continuity of the function 
. β 
β
A)
is discontinuous at 
.
B)
is discontinuous at 
.
C)
is discontinuous at 
.
D)
is continuous for all real x.
E)
is continuous at 
.
. β βA)
is discontinuous at .B)
is discontinuous at .C)
is discontinuous at .D)
is continuous for all real x.E)
is continuous at . Question
Find the x-values (if any)at which 
is not continuous. β
A)
is not continuous at 
and the discontinuity is nonremovable.
B)
is not continuous at 
and the discontinuity is removable.
C)
is continuous for all real 
.
D)
is not continuous at 
and the discontinuity is removable.
E)
is not continuous at 
and
is a removable discontinuity.
is not continuous. βA)
is not continuous at and the discontinuity is nonremovable.B)
is not continuous at and the discontinuity is removable.C)
is continuous for all real .D)
is not continuous at and the discontinuity is removable.E)
is not continuous at and is a removable discontinuity. Question
Find the x-values (if any)at which the function 
is not continuous.Which of the discontinuities are removable? β
A)
,removable
B)
,removable
C)
,not removable
D)continuous everywhere
E)
,removable
is not continuous.Which of the discontinuities are removable? βA)
,removableB)
,removableC)
,not removableD)continuous everywhere
E)
,removable Question
Find all values of c such that f is continuous on 
. β 
β
A)
B)
C)
D)
, 
E)
, 
. β βA)
B)
C)
D)
, E)
, Question
Find the x-values (if any)at which 
is not continuous. β
A)
is not continuous at 
and
has a removable discontinuity at
.
B)
is not continuous at 
and both the discontinuities are nonremovable.
C)
is not continuous at 
and
has a removable discontinuity at
.
D)
is not continuous at 
and
has a removable discontinuity at
.
E)
is continuous for all real x.
is not continuous. βA)
is not continuous at and has a removable discontinuity at .B)
is not continuous at and both the discontinuities are nonremovable.C)
is not continuous at and has a removable discontinuity at .D)
is not continuous at and has a removable discontinuity at .E)
is continuous for all real x. Question
Find the x-values (if any)at which the function 
is not continuous.Which of the discontinuities are removable? β
A)4 and -4,removable
B)discontinuous everywhere 0 00
C)continuous everywhere 0 00
D)4 and -4,not removable
E)0,removable
is not continuous.Which of the discontinuities are removable? βA)4 and -4,removable
B)discontinuous everywhere 0 00
C)continuous everywhere 0 00
D)4 and -4,not removable
E)0,removable
Question
Find the limit. β 
β
A)
B)0
C)
D)
E)
βA)
B)0
C)
D)
E)
Question
Find the limit. β 
β
A)75
B)-5
C)-75
D)5
E)45
βA)75
B)-5
C)-75
D)5
E)45
Question
Find the limit. β 
β
A)6
B)-6
C)24
D)-24
E)0
βA)6
B)-6
C)24
D)-24
E)0
Question
Find the lmit. β 
β
A)
B)
C)
D)
E)does not exist
βA)
B)
C)
D)
E)does not exist
Question
Find the limit. β 
β
A)
B)
C)
D)
E)0
βA)
B)
C)
D)
E)0
Question
Find the constant 
such that the function β 
β
Is continuous on the entire real line.
β
A)1
B)-8
C)8
D)-15
E)15
such that the function β βIs continuous on the entire real line.
β
A)1
B)-8
C)8
D)-15
E)15
Question
Find the limit. β 
β
A)
B)
C)
D)
E)
βA)
B)
C)
D)
E)
Question
Find the limit (if it exists).Note that 
represents the greatest integer function. β 
β
A)3
B)Limit does not exist.
C)2
D)0
E)1
represents the greatest integer function. β βA)3
B)Limit does not exist.
C)2
D)0
E)1
Unlock Deck
Sign up to unlock the cards in this deck!
Unlock Deck
Unlock Deck
1/119
Play
Full screen (f)
Deck 2: Limits and Their Properties
1
For the function ,use a graphing utility to complete the table and estimate the limit as x approaches infinity. x
100
101
102
103
104
105
106 β
A)1.0000
B)2.2500
C)3.4300
D)0.3500
E)does not exist
,use a graphing utility to complete the table and estimate the limit as x approaches infinity. x100
101
102
103
104
105
106
βA)1.0000
B)2.2500
C)3.4300
D)0.3500
E)does not exist
1.0000
2
Find the limit. β β
A)
B)-4
C)
D)4
E)-1
βA)
B)-4
C)
D)4
E)-1
-1
3
βUse the graphs of and given below to answer the following question:
β
Is β continuous at ? Explain why or why not.
and given below to answer the following question:β
Is
β continuous at ? Explain why or why not.
. 
. 
is defined.The 
since the values from the right and the left are the same.Since 
is equal to -1,the limit exists and 
.Yes, 
β continuous at 
β.β
4
What is β? Explain your reasoning.
β? Explain your reasoning. Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
5
If β ,what is βkβ so that is continuous at ?
β ,what is βkβ so that is continuous at ? Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
6
βFind the limit,if it exists: . β
A)β
B)β
C)β
D)βThe limit does not exist.
. βA)β
B)β
C)β
D)βThe limit does not exist.
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
7
For the function ,use a graphing utility to complete the table and estimate the limit as x approaches infinity. x
100
101
102
103
104
105
106 β
A)3
B)-2
C)8
D)0
E)None of the above
,use a graphing utility to complete the table and estimate the limit as x approaches infinity. x100
101
102
103
104
105
106
βA)3
B)-2
C)8
D)0
E)None of the above
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
8
βEstimate the limit,if it exists: where is represented by the given graph: β β
A)β-2
B)β1
C)β-3
D)βThe limit does not exist.
where is represented by the given graph: β βA)β-2
B)β1
C)β-3
D)βThe limit does not exist.
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
9
βHow many vertical asymptotes exist for the function in the open interval ? β
A)β4
B)β1
C)β2
D)β3
in the open interval ? βA)β4
B)β1
C)β2
D)β3
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
10
Evaluate the limit,if it exists:β . β
A)β-17
B)β-9
C)β17
D)βThe limit does not exist.
. βA)β-17
B)β-9
C)β17
D)βThe limit does not exist.
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
11
Evaluate the limit,if it exists:β . β
A)β
B)β
C)β
D)βThe limit does not exist.
. βA)β
B)β
C)β
D)βThe limit does not exist.
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
12
βFor what value of k is the function continuous at ? β
A)β
B)β0
C)β
D)β
continuous at ? βA)β
B)β0
C)β
D)β
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
13
βWhich of the following statements is true? β
A)β .
B)β does not exist.
C)β does not exist.
D)β .
A)β
.B)β
does not exist.C)β
does not exist.D)β
. Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
14
βIf is a continuous function on the closed interval ,with and c is in the closed interval ,then which of the following statements must be true? β
A)β
B)β
C)βThere is at least one value c such that .
D)βThere is only one value c such that .
is a continuous function on the closed interval ,with and c is in the closed interval ,then which of the following statements must be true? βA)β
B)β
C)βThere is at least one value c such that
.D)βThere is only one value c such that
. Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
15
For the function ,use a graphing utility to complete the table and estimate the limit as x approaches infinity. x
100
101
102
103
104
105
106 β
A)1.3333
B)2.3333
C)0.7500
D)1.7500
E)-0.2500
,use a graphing utility to complete the table and estimate the limit as x approaches infinity. x100
101
102
103
104
105
106
βA)1.3333
B)2.3333
C)0.7500
D)1.7500
E)-0.2500
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
16
Identify the vertical asymptotes for . β
A)β ,
B)β
C)β
D)β ,
. βA)β
,B)β
C)β
D)β
, Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
17
βEvaluate the limit,if it exists: . β
A)β
B)β
C)β
D)βThe limit does not exist.
. βA)β
B)β
C)β
D)βThe limit does not exist.
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
18
Is β continuous at ? Explain why or why not.
β continuous at ? Explain why or why not. Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
19
βEvaluate the limit,if it exists: . β
A)β
B)β
C)β
D)β
. βA)β
B)β
C)β
D)β
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
20
βGiven the function .What value of k will make this piecewise function continuous? β
A)β
B)β
C)β
D)β
.What value of k will make this piecewise function continuous? βA)β
B)β
C)β
D)β
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
21
Find the limit. β β
A)
B)-6
C)0
D)
E)
βA)
B)-6
C)0
D)
E)
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
22
A rectangular page is to contain 144 square inches of print.The margins on each side are 1 inch.Find the dimensions of the page such that the least amount of paper is used. β
A)16,16
B)13,13
C)15,15
D)25,25
E)14,14
A)16,16
B)13,13
C)15,15
D)25,25
E)14,14
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
23
Find all the vertical asymptotes (if any)of the graph of the function . β
A)
B)
C)
D)
E)no vertical asymptotes
. βA)
B)
C)
D)
E)no vertical asymptotes
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
24
The graph shows the temperature T,in degrees Fahrenheit,of molten glass t seconds after it is removed from a kiln. β β
Find .
β
A)1,515Β°
B)65Β°
C)1,450Β°
D)82Β°
E)1,385Β°
βFind
.β
A)1,515Β°
B)65Β°
C)1,450Β°
D)82Β°
E)1,385Β°
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
25
Sketch the graph of the function using any extrema,intercepts,symmetry,and asymptotes. β
A)β
B)β
C)β
D)β
E)β
using any extrema,intercepts,symmetry,and asymptotes. βA)β
B)β
C)β
D)β
E)β
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
26
Find the limit. β β
A)1
B)0
C)
D)
E)does not exist
βA)1
B)0
C)
D)
E)does not exist
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
27
Find all the vertical asymptotes (if any)of the graph of the function . β
A)
B)
C)
D)
E)no vertical asymptotes
. βA)
B)
C)
D)
E)no vertical asymptotes
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
28
Find the point on the graph of the function that is closest to the point . β
A)
B)
C)
D)
E)
that is closest to the point . βA)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
29
Find the limit. β β
A)
B)
C)1
D)3
E)
βA)
B)
C)1
D)3
E)
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
30
Sketch the graph of the relation using any extrema,intercepts,symmetry,and asymptotes. β
A)β
B)β
C)β
D)β
E)β
using any extrema,intercepts,symmetry,and asymptotes. βA)β
B)β
C)β
D)β
E)β
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
31
Find the limit. β β
A)
B)
C)1
D)-5
E)
βA)
B)
C)1
D)-5
E)
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
32
Sketch the graph of the function using any extrema,intercepts,symmetry,and asymptotes. β
A)β
B)β
C)β
D)β
E)β
using any extrema,intercepts,symmetry,and asymptotes. βA)β
B)β
C)β
D)β
E)β
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
33
Sketch the graph of the relation using any extrema,intercepts,symmetry,and asymptotes. β
A)β
B)β
C)β
D)β
E)β
using any extrema,intercepts,symmetry,and asymptotes. βA)β
B)β
C)β
D)β
E)β
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
34
A heat probe is attached to the heat exchanger of a heating system.The temperature T (in degrees Celsius)is recorded t seconds after the furnace is started.A model for the data recorded for the first two minutes is given by .Find . β
A)1,499Β°
B)1,411Β°
C)50Β°
D)88Β°
E)28Β°
.Find . βA)1,499Β°
B)1,411Β°
C)50Β°
D)88Β°
E)28Β°
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
35
Find all the vertical asymptotes (if any)of the graph of the function . β
A)
B)
C)
D) ,
E)no vertical asymptotes
. βA)
B)
C)
D)
, E)no vertical asymptotes
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
36
A container holds 6 liters of a 25% brine solution.A model for the concentration C of the mixture after adding x liters of an 0.89% brine solution to the container and then draining x liters of the well-mixed solution is given as .Find .Round your answer to two decimal places. β
A)0.67%
B)0.33%
C)0.93%
D)0.89%
E)0.25%
.Find .Round your answer to two decimal places. βA)0.67%
B)0.33%
C)0.93%
D)0.89%
E)0.25%
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
37
A business has a cost of for producing x units.The average cost per unit is .Find the limit of as x approaches infinity. β
A)375.0
B)1
C)600
D)0
E)1.6
for producing x units.The average cost per unit is .Find the limit of as x approaches infinity. βA)375.0
B)1
C)600
D)0
E)1.6
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
38
Find the point on the graph of the function that is closest to the point .Round all numerical values in your answer to four decimal places. β
A)
B)
C)
D)
E)
that is closest to the point .Round all numerical values in your answer to four decimal places. βA)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
39
Find the vertical asymptotes (if any)of the function . β
A)
B)
C)β
D)
E)
. βA)
B)
C)β
D)
E)
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
40
Find the limit. β β
A)
B)1
C)0
D)
E)
βA)
B)1
C)0
D)
E)
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
41
Use the graph to determine the following limits,and discuss the continuity of the function at . (i) (ii) (iii) β
A)1,-1,does not exist,not continuous
B)1,0,does not exist,not continuous
C)0,1,does not exist,not continuous
D)-4,0,does not exist,not continuous
E)0,1,0,continuous
. (i) (ii) (iii) β A)1,-1,does not exist,not continuous
B)1,0,does not exist,not continuous
C)0,1,does not exist,not continuous
D)-4,0,does not exist,not continuous
E)0,1,0,continuous
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
42
Find the limit. β β
A)
B)
C)4
D)-2
E)-4
βA)
B)
C)4
D)-2
E)-4
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
43
A petrol car is parked 35 feet from a long warehouse (see figure).The revolving light on top of the car turns at a rate of revolution per second.The rate at which the light beam moves along the wall is ft/sec.Find the rate r when ΞΈ is . β ft
β
A) ft/sec
B) ft/sec
C) ft/sec
D) ft/sec
E) ft/sec
revolution per second.The rate at which the light beam moves along the wall is ft/sec.Find the rate r when ΞΈ is . β ftβ
A)
ft/secB)
ft/secC)
ft/secD)
ft/secE)
ft/sec Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
44
Find all vertical asymptotes (if any)of the function . β
A)
B)
C)
D)
E)
. βA)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
45
Find the limit (if it exists). β β
A)
B)0
C)Limit does not exist.
D)
E)
βA)
B)0
C)Limit does not exist.
D)
E)
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
46
Use the graph as shown to determine the following limits,and discuss the continuity of the function at . β
(i) (ii) (iii) β β
A)2,2,2,not continuous
B)3,3,3,continuous
C)4,4,4,not continuous
D)3,3,3,not continuous
E)2,2,2,continuous
. β(i)
(ii) (iii) β βA)2,2,2,not continuous
B)3,3,3,continuous
C)4,4,4,not continuous
D)3,3,3,not continuous
E)2,2,2,continuous
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
47
A 35-foot ladder is leaning against a house (see figure).If the base of the ladder is pulled away from the house at a rate of 2 feet per second,the top will move down the wall at a rate of ft/sec,where x is the distance between the base of the ladder and the house.Find the rate r when x is 28 feet. β ft
β
A) ft/sec
B) ft/sec
C) ft/sec
D) ft/sec
E) ft/sec
ft/sec,where x is the distance between the base of the ladder and the house.Find the rate r when x is 28 feet. β ftβ
A)
ft/secB)
ft/secC)
ft/secD)
ft/secE)
ft/sec Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
48
Use the graph as shown to determine the following limits,and discuss the continuity of the function at . β
(i) (ii) (iii) β β
A)3,3,3,continuous
B)2,2,2,not continuous
C)3,3,3,not continuous
D)-3,-3,-3,continuous
E)2,2,2,continuous
. β(i)
(ii) (iii) β βA)3,3,3,continuous
B)2,2,2,not continuous
C)3,3,3,not continuous
D)-3,-3,-3,continuous
E)2,2,2,continuous
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
49
A 20-foot ladder is leaning against a house (see figure).If the base of the ladder is pulled away from the house at a rate of 2 feet per second,the top will move down the wall at a rate of ft/sec,where x is the distance between the base of the ladder and the house.Find the limit of r as . β ft
β
A)
B)40
C)0
D)
E)20
ft/sec,where x is the distance between the base of the ladder and the house.Find the limit of r as . β ftβ
A)
B)40
C)0
D)
E)20
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
50
Find the limit (if it exists). β ,where β
A)Limit does not exist.
B)0
C)5
D)6
E)15
,where βA)Limit does not exist.
B)0
C)5
D)6
E)15
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
51
Use a graphing utility to graph the function and determine the following one-sided limit. β β
A)
B)4
C)-4
D)
E)0
and determine the following one-sided limit. β βA)
B)4
C)-4
D)
E)0
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
52
Find the limit (if it exists).Note that represents the greatest integer function. β β
A)3
B)-2
C)2
D)-3
E)does not exist
represents the greatest integer function. β βA)3
B)-2
C)2
D)-3
E)does not exist
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
53
Find the limit. β β
A)1
B)0
C)-1
D)
E)
βA)1
B)0
C)-1
D)
E)
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
54
Find the following limit if it exists: .Use when appropriate. β
A)
B)4
C)1
D)
E)does not exist
.Use when appropriate. βA)
B)4
C)1
D)
E)does not exist
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
55
Use a graphing utility to graph the function and determine the one-sided limit . β
A)
B)
C)0
D)3
E)2
and determine the one-sided limit . βA)
B)
C)0
D)3
E)2
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
56
Find the vertical asymptotes (if any)of the function . β
A)
B)
C)
D)
E)no vertical asymptotes
. βA)
B)
C)
D)
E)no vertical asymptotes
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
57
Find the limit (if it exists). β β
A)0
B)
C)
D)
E)Limit does not exist.
βA)0
B)
C)
D)
E)Limit does not exist.
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
58
A petrol car is parked 65 feet from a long warehouse (see figure).The revolving light on top of the car turns at a rate of revolution per second.The rate at which the light beam moves along the wall is ft/sec.Find the limit of r as . ββ β β ft
β
A)
B)
C)0
D)65
E)
revolution per second.The rate at which the light beam moves along the wall is ft/sec.Find the limit of r as . ββ β β ftβ
A)
B)
C)0
D)65
E)
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
59
Find the limit. β β
A)1
B)
C)0
D)
E)β-1
βA)1
B)
C)0
D)
E)β-1
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
60
Find the limit (if it exists). β β
A)
B)
C)0
D)
E)Limit does not exist.
βA)
B)
C)0
D)
E)Limit does not exist.
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
61
Find the value of c guaranteed by the Intermediate Value Theorem. β , , β
A)0
B)2
C)4
D)1
E)3
, , βA)0
B)2
C)4
D)1
E)3
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
62
Find the x-values (if any)at which the function is not continuous.Which of the discontinuities are removable? β
A)no points of discontinuity
B) (not removable), (removable)
C) (removable), (not removable)
D)no points of continuity
E) (not removable), (not removable)
is not continuous.Which of the discontinuities are removable? βA)no points of discontinuity
B)
(not removable), (removable)C)
(removable), (not removable)D)no points of continuity
E)
(not removable), (not removable) Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
63
Find the value of c guaranteed by the Intermediate Value Theorem. β , , β
A)13
B)4
C)3
D)11
E)12
, , βA)13
B)4
C)3
D)11
E)12
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
64
Find the limit. β β
A)
B)
C)
D)
E)does not exist
βA)
B)
C)
D)
E)does not exist
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
65
Find the constant a such that the function β β
Is continuous on the entire real line.
β
A) ,
B) ,
C) ,
D) ,
E) ,
βIs continuous on the entire real line.
β
A)
, B)
, C)
, D)
, E)
, Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
66
A long distance phone service charges $0.45 for the first 11 minutes and $0.1 for each additional minute or fraction thereof.Use the greatest integer function to write the cost C of a call in terms of time t (in minutes). β
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
67
Discuss the continuity of the function . β β
A) is discontinuous at .
B) is discontinuous at .
C) is discontinuous at .
D) is continuous for all real x.
E) is continuous at .
. β βA)
is discontinuous at .B)
is discontinuous at .C)
is discontinuous at .D)
is continuous for all real x.E)
is continuous at . Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
68
Find the x-values (if any)at which is not continuous. β
A) is not continuous at and the discontinuity is nonremovable.
B) is not continuous at and the discontinuity is removable.
C) is continuous for all real .
D) is not continuous at and the discontinuity is removable.
E) is not continuous at and
is a removable discontinuity.
is not continuous. βA)
is not continuous at and the discontinuity is nonremovable.B)
is not continuous at and the discontinuity is removable.C)
is continuous for all real .D)
is not continuous at and the discontinuity is removable.E)
is not continuous at and is a removable discontinuity. Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
69
Find the x-values (if any)at which the function is not continuous.Which of the discontinuities are removable? β
A) ,removable
B) ,removable
C) ,not removable
D)continuous everywhere
E) ,removable
is not continuous.Which of the discontinuities are removable? βA)
,removableB)
,removableC)
,not removableD)continuous everywhere
E)
,removable Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
70
Find all values of c such that f is continuous on . β β
A)
B)
C)
D) ,
E) ,
. β βA)
B)
C)
D)
, E)
, Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
71
Find the x-values (if any)at which is not continuous. β
A) is not continuous at and
has a removable discontinuity at
.
B) is not continuous at and both the discontinuities are nonremovable.
C) is not continuous at and
has a removable discontinuity at
.
D) is not continuous at and
has a removable discontinuity at
.
E) is continuous for all real x.
is not continuous. βA)
is not continuous at and has a removable discontinuity at .B)
is not continuous at and both the discontinuities are nonremovable.C)
is not continuous at and has a removable discontinuity at .D)
is not continuous at and has a removable discontinuity at .E)
is continuous for all real x. Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
72
Find the x-values (if any)at which the function is not continuous.Which of the discontinuities are removable? β
A)4 and -4,removable
B)discontinuous everywhere 0 00
C)continuous everywhere 0 00
D)4 and -4,not removable
E)0,removable
is not continuous.Which of the discontinuities are removable? βA)4 and -4,removable
B)discontinuous everywhere 0 00
C)continuous everywhere 0 00
D)4 and -4,not removable
E)0,removable
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
73
Find the limit. β β
A)
B)0
C)
D)
E)
βA)
B)0
C)
D)
E)
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
74
Find the limit. β β
A)75
B)-5
C)-75
D)5
E)45
βA)75
B)-5
C)-75
D)5
E)45
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
75
Find the limit. β β
A)6
B)-6
C)24
D)-24
E)0
βA)6
B)-6
C)24
D)-24
E)0
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
76
Find the lmit. β β
A)
B)
C)
D)
E)does not exist
βA)
B)
C)
D)
E)does not exist
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
77
Find the limit. β β
A)
B)
C)
D)
E)0
βA)
B)
C)
D)
E)0
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
78
Find the constant such that the function β β
Is continuous on the entire real line.
β
A)1
B)-8
C)8
D)-15
E)15
such that the function β βIs continuous on the entire real line.
β
A)1
B)-8
C)8
D)-15
E)15
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
79
Find the limit. β β
A)
B)
C)
D)
E)
βA)
B)
C)
D)
E)
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
80
Find the limit (if it exists).Note that represents the greatest integer function. β β
A)3
B)Limit does not exist.
C)2
D)0
E)1
represents the greatest integer function. β βA)3
B)Limit does not exist.
C)2
D)0
E)1
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
Unlock Deck
k this deck
Unlock Deck
Unlock for access to all 119 flashcards in this deck.
