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Deck 11: Mechanical Ventilation and Sedation: Assessment, Medications, and Complications
Full screen (f)
Question
Consider the curve defined by the parametric equations 
and 
.For any time t, 
A)
B)
C)
D)
and .For any time t, A)
B)
C)
D)
Question
If 
on the interval 
,then what is the value of c on the interval 
that satisfies the Mean Value Theorem?
A)
B)
C)
D)
on the interval ,then what is the value of c on the interval that satisfies the Mean Value Theorem? A)
B)
C)
D)
Question
Let 
.Which of the following values are x-intercepts of the graph of 
?
A)
B)
C)
D)
.Which of the following values are x-intercepts of the graph of ? A)
B)
C)
D)
Question
Let 
.The first two nonzero terms of the Taylor expansion for 
about 
are
A)
B)
C)
D)
.The first two nonzero terms of the Taylor expansion for about are A)
B)
C)
D)
Question
Let 
.Which of the following integral expressions represents the area between 
and the horizontal axis on the interval 
?
A)
B)
C)
D)
.Which of the following integral expressions represents the area between and the horizontal axis on the interval ? A)
B)
C)
D)
Question
Which one of the following statements is false?
A)
diverges.
B)
diverges.
C)
converges.
D)
converges absolutely.
A)
diverges.B)
diverges.C)
converges.D)
converges absolutely. Question
If 
and 
,then find the value of a such that 
.
A)
B)
C)
D)
and ,then find the value of a such that . A)
B)
C)
D)
Question
Let 
.The first three terms of the Maclaurin series for 
are
A)
B)
C)
D)
.The first three terms of the Maclaurin series for are A)
B)
C)
D)
Question
Let 
on the interval 
The absolute maximum of 
on this interval is
A)
B)
C)
D)e
on the interval The absolute maximum of on this interval is A)
B)
C)
D)e
Question
What are all values of x for which the series 
converges?
A)The series converges for
only.
B)
C)
D)
converges? A)The series converges for
only.B)
C)
D)
Question
If 
is a function which is increasing and concave down on the interval 
,then which of the following could be the graph of 
?
A)
B)
C)
D)
is a function which is increasing and concave down on the interval ,then which of the following could be the graph of ? A)
B)
C)
D)
Question
The tangent line to the curve 
at 
intersects the x-axis at 
A)
B)
C)-2
D)
at intersects the x-axis at A)
B)
C)-2
D)
Question
A particle moves in the xy-plane such that its velocity vector for time 
is , 
.If the particle is at the point 
when 
,then what is the position vector of the particle when 
?
A)
B)
C)
D)
is , .If the particle is at the point when ,then what is the position vector of the particle when ? A)
B)
C)
D)
Question
A particle moves in the xy-plane for time 
according to the parametric equations 
and 
.Which of the following statements about the particle are true?
I.
The particle is moving to the right when
.
II.
The particle is moving upward when
.
III.
The particle is at rest when
A)I only
B)I and II only
C)II and III only
D)I,II,and III
according to the parametric equations and .Which of the following statements about the particle are true? I.
The particle is moving to the right when
.II.
The particle is moving upward when
.III.
The particle is at rest when
A)I only
B)I and II only
C)II and III only
D)I,II,and III
Question
If 
,then the slope of the tangent line to 
at 
is
A)-21
B)0
C)21
D)undefined
,then the slope of the tangent line to at is A)-21
B)0
C)21
D)undefined
Question
The Maclaurin series 
represents the function 
A)
B)
C)
D)
represents the function A)
B)
C)
D)
Question
The first four terms of the Taylor expansion for 
about 
are 
.What is the value of 
?
A)
B)
C)
D)
about are .What is the value of ? A)
B)
C)
D)
Question
Let 
be the solution to the differential equation 
.Using Euler's method,starting at the point 
− with step size 
,what is the approximate value of 
?
A)8.75
B)-0.75
C)-2.25
D)-1.5
be the solution to the differential equation .Using Euler's method,starting at the point − with step size ,what is the approximate value of ? A)8.75
B)-0.75
C)-2.25
D)-1.5
Question
If y is a function of x such that 
and 
,then 
A)
B)
C)
D)
and ,then A)
B)
C)
D)
Question
If 
,then 
A)
B)
C)
D)
,then A)
B)
C)
D)
Question
If 
is a function defined on 
such that 
,then which of the following could be the graph of 
?
A)
B)
C)
D)
is a function defined on such that ,then which of the following could be the graph of ? A)
B)
C)
D)
Question
Find all values of x in the open interval 
such that 
.
such that . Question
A particle moves in the xy-plane according to the parametric equations 
and 
for 
.What is the average speed of the particle during the time interval 
?
A)7.187
B)6.468
C)7.906
D)6.047
and for .What is the average speed of the particle during the time interval ? A)7.187
B)6.468
C)7.906
D)6.047
Question
The vertical line 
divides region R into two regions with equal areas.Write,but do not solve,an equation involving integral expressions whose solution gives the value 
.
divides region R into two regions with equal areas.Write,but do not solve,an equation involving integral expressions whose solution gives the value . Question
Which of the following gives the length of the curve 
over the closed interval 
A)
B)
C)
D)
over the closed interval A)
B)
C)
D)
Question
Consider the function
defined on the closed interval whose endpoints are 
and 
.
Find the absolute maximum of
on this interval.Justify your answer.Round your answer to 3 decimals.
Consider the function
defined on the closed interval whose endpoints are and .Find the absolute maximum of
on this interval.Justify your answer.Round your answer to 3 decimals. Question
Question
What is the area enclosed by the lemniscate 
?
A)50
B)
C)
D)25
? A)50
B)
C)
D)25
Question
If 
and 
,then 
A)
B)
C)
D)
and ,then A)
B)
C)
D)
Question
Oil is pumped continuously from a certain oil well at a rate modeled by the function 
.Let t be the number of days for a 25-day period and let 
be measured in barrels per day.To the nearest barrel,according to the model,how much oil will be pumped from the well from the 11th day to the 22nd day?
A)-33,275
B)45,829
C)21,629
D)52,907
.Let t be the number of days for a 25-day period and let be measured in barrels per day.To the nearest barrel,according to the model,how much oil will be pumped from the well from the 11th day to the 22nd day? A)-33,275
B)45,829
C)21,629
D)52,907
Question
A particle moves along the x-axis so that its acceleration is 
for 
.If the initial velocity of the particle is 12,then what is the average velocity of the particle during the time interval 
?
A)36.955
B)35.045
C)61.045
D)37.045
for .If the initial velocity of the particle is 12,then what is the average velocity of the particle during the time interval ? A)36.955
B)35.045
C)61.045
D)37.045
Question
You may use a calculator for any problem in this section. 
Let R be the region enclosed by the graph of
and the horizontal line 
,as shown in the figure above.
Find the volume of the solid generated when R is rotated about the line
.Round your answer to 3 decimal places.
Let R be the region enclosed by the graph of
and the horizontal line ,as shown in the figure above.Find the volume of the solid generated when R is rotated about the line
.Round your answer to 3 decimal places.
Question
Question
A particle moves along the x-axis such that its velocity is given by 
for time 
.If the particle has position 15 when 
,then what is its position when it comes to rest for the first time?
A)14.889
B)14.188
C)16.094
D)14.594
for time .If the particle has position 15 when ,then what is its position when it comes to rest for the first time? A)14.889
B)14.188
C)16.094
D)14.594
Question
You may use a calculator for any problem in this section. 
The rate that water flows into two identical tanks during a 24-hour period is given by the models below.Both
and 
are measured in gallons per hour for 
hours,and both tanks are empty at time t = 0.
Tank 1: The graph of
consists of the line segments indicated in the figure.
Tank 2:
What is the value of
? What is the value of 
? Give units for both answers.Round your answer to 3 decimal places.
___________
___________
The rate that water flows into two identical tanks during a 24-hour period is given by the models below.Both
and are measured in gallons per hour for hours,and both tanks are empty at time t = 0.Tank 1: The graph of
consists of the line segments indicated in the figure.Tank 2:
What is the value of
? What is the value of ? Give units for both answers.Round your answer to 3 decimal places.
___________
___________ Question
What is the value of 
.
A)
B)
C)
D)Does not exist
. A)
B)
C)
D)Does not exist
Question
Let 
.If 
represents the nth derivative of 
,then what is 
?
A)
B)
C)
D)
.If represents the nth derivative of ,then what is ? A)
B)
C)
D)
Question
For the function 
, 
.If 
is the inverse of 
,what is the slope of the tangent to 
at the point 
?
A)0.276
B)0.226
C)0.251
D)0.211
, .If is the inverse of ,what is the slope of the tangent to at the point ? A)0.276
B)0.226
C)0.251
D)0.211
Question
During the 24-hour period,is there ever a time other than 
when the amount of water in the two tanks is the same? If yes,find all such values of 
.If no,explain why not.If needed,round your answer to 3 decimal places.
when the amount of water in the two tanks is the same? If yes,find all such values of .If no,explain why not.If needed,round your answer to 3 decimal places. Question
Question
The graph of 
is pictured below.Which of the following statements about 
are true? 
i.A left endpoint approximation is greater than
.II.A right endpoint approximation is less than 
.III.A trapezoidal approximation is less than 
A)None are true
B)III only
C)I and III only
D)I,II,and III
is pictured below.Which of the following statements about are true? i.A left endpoint approximation is greater than
.II.A right endpoint approximation is less than .III.A trapezoidal approximation is less than A)None are true
B)III only
C)I and III only
D)I,II,and III
Question
Let
.
Find all values of
for which 
converges.
Let
.Find all values of
for which converges. Question
The equation of the tangent line to the function 
at 
is
A)
B)
C)
D)
at is A)
B)
C)
D)
Question
Use the values to sketch a slope field for 
on the axes provided.
A)
B)
C)
D)
on the axes provided. A)
B)
C)
D)
Question
Use the first three terms of 
to estimate the value of 
.Round your answer to 3 decimal places.
to estimate the value of .Round your answer to 3 decimal places. Question
A particle moves in the xy-plane with position for all real values of 
given by the parametric equations 
and 
.
Give the coordinates of the velocity vector for any time
.
given by the parametric equations and .Give the coordinates of the velocity vector for any time
. Question
Consider the differential equation 
,where 
is the solution to the equation and 
.Using Euler's method starting at 
with step size 
,what is the approximation for 
?
A)-3.5
B)-3
C)-2.5
D)-2
,where is the solution to the equation and .Using Euler's method starting at with step size ,what is the approximation for ? A)-3.5
B)-3
C)-2.5
D)-2
Question
Question
Is the particle moving to the left or right when 
? Is the particle moving up or down when 
?
A)left and up
B)left and down
C)right and up
D)right and down
? Is the particle moving up or down when ? A)left and up
B)left and down
C)right and up
D)right and down
Question
Determine the point(s)of inflection for 
.
. Question
Question
Evaluate 
.
A)0
B)1
C)2e
D)∞
. A)0
B)1
C)2e
D)∞
Question
The position vector for a particle moving in the 
-plane for 
is 1st The slope of the tangent line to the path of the particle at 
is
A)
B)
C)
D)162.5
-plane for is 1st The slope of the tangent line to the path of the particle at is A)
B)
C)
D)162.5
Question
If 
,then 
A)
B)
C)
D)
,then A)
B)
C)
D)
Question
What is the slope of the path of the particle when 
?
? Question
Show that 
is a solution to the differential equation 
.
is a solution to the differential equation . Question
Find the particular solution 
.
. Question
Find the limit 
.
A)0
B)
C)
D)∞
. A)0
B)
C)
D)∞
Question
Using Euler's method starting at 
with step size 
,estimate the value of 
.
with step size ,estimate the value of .
Question
If 
is a function such that 
is increasing for 
and 
is decreasing for 
,then which of the following could be the graph of 
?
A)
B)
C)
D)
is a function such that is increasing for and is decreasing for ,then which of the following could be the graph of ? A)
B)
C)
D)
Question
Which of the following series converge?
i.
II. 
III. 
A)I only
B)I and II
C)I and III
D)I,II,and III
i.
II. III. A)I only
B)I and II
C)I and III
D)I,II,and III
Question
If 
and 
,then 
A)
B)
C)
D)
and ,then A)
B)
C)
D)
Question
The acceleration vector of a particle moving in the 
-plane is 
,for 
.If the velocity vector at 
is 
,then how fast is the particle moving when 
?
A)5
B)6
C)
D)
-plane is ,for .If the velocity vector at is ,then how fast is the particle moving when ? A)5
B)6
C)
D)
Question
The graph of 
has inflection points at 
A)-
and
only.
B)0 and
only.
C)0 and
only.
D)-
,0 and
.
has inflection points at A)-
and only.B)0 and
only.C)0 and
only.D)-
,0 and . Question
If 
,then 
A)
B)
C)
D)
,then A)
B)
C)
D)
Question
What are all the values of 
for which the series 
converges?
A)
B)
C)
D)
for which the series converges? A)
B)
C)
D)
Question
The graph of 
below,consisting of a pair of line segments,is pictured below. 
If
,then 
A)3
B)4
C)4.5
D)5.5
below,consisting of a pair of line segments,is pictured below. If
,then A)3
B)4
C)4.5
D)5.5
Question
Let
,where 
is pictured above.
What is the domain of
?
A)All real numbers except -1 and 5
B)
C)
D)
Let
,where is pictured above.
What is the domain of
? A)All real numbers except -1 and 5
B)
C)
D)
Question
The volume of the solid generated by revolving the region enclosed between the graph of 
and the lines 
and 
about the 
-axis is given by which integral expression?
A)
B)
C)
D)
and the lines and about the -axis is given by which integral expression? A)
B)
C)
D)
Question
The area enclosed by the polar curve 
in the interval 
is
A)
B)
C)
D)
in the interval is A)
B)
C)
D)
Question
A particle moves in the 
-plane according to the parametric equations 
and 
.An expression for the length of the path of the particle from 
to 
is
A)
B)
C)
D)
-plane according to the parametric equations and .An expression for the length of the path of the particle from to is A)
B)
C)
D)
Question
The general solution to the differential equation 
is 
A)
B)
C)
D)
is A)
B)
C)
D)
Question
Evaluate the limit,if it exists: 
.
A)0
B)1
C)-1
D)The limit does not exist
. A)0
B)1
C)-1
D)The limit does not exist
Question
The first four terms of the Taylor expansion for 
about 
are 
.What is the value of 
?
A)- 6
B)- 3
C)-
D)-
about are .What is the value of ? A)- 6
B)- 3
C)-
D)-
Question
Let 
.The first four nonzero terms of the Taylor approximation for 
about 
are
A)
B)
C)
D)
.The first four nonzero terms of the Taylor approximation for about are A)
B)
C)
D)
Question
What is the slope of the curve 
at the point 
?
A)
B)
C)
D)
at the point ? A)
B)
C)
D)
Question
The slope field at the bottom represents an approximation to the general solution to which differential equation? 
A)
B)
C)
D)
A)
B)
C)
D)
Question
What is the value of 
?
A)0
B)1
C)2
D)4
? A)0
B)1
C)2
D)4
Question
The slope of the normal line to 
at 
is
A)
B)0
C)
D)10
at is A)
B)0
C)
D)10
Question
Which expression below represents the first four terms of the Maclaurin approximation to the area under the curve 
from 
to 
?
A)
B)
C)
D)
from to ? A)
B)
C)
D)
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Deck 11: Mechanical Ventilation and Sedation: Assessment, Medications, and Complications
1
Consider the curve defined by the parametric equations and .For any time t,
A)
B)
C)
D)
and .For any time t, A)
B)
C)
D)
2
If on the interval ,then what is the value of c on the interval that satisfies the Mean Value Theorem?
A)
B)
C)
D)
on the interval ,then what is the value of c on the interval that satisfies the Mean Value Theorem? A)
B)
C)
D)
3
Let .Which of the following values are x-intercepts of the graph of ?
A)
B)
C)
D)
.Which of the following values are x-intercepts of the graph of ? A)
B)
C)
D)
4
Let .The first two nonzero terms of the Taylor expansion for about are
A)
B)
C)
D)
.The first two nonzero terms of the Taylor expansion for about are A)
B)
C)
D)
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5
Let .Which of the following integral expressions represents the area between and the horizontal axis on the interval ?
A)
B)
C)
D)
.Which of the following integral expressions represents the area between and the horizontal axis on the interval ? A)
B)
C)
D)
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6
Which one of the following statements is false?
A) diverges.
B) diverges.
C) converges.
D) converges absolutely.
A)
diverges.B)
diverges.C)
converges.D)
converges absolutely. Unlock Deck
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7
If and ,then find the value of a such that .
A)
B)
C)
D)
and ,then find the value of a such that . A)
B)
C)
D)
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8
Let .The first three terms of the Maclaurin series for are
A)
B)
C)
D)
.The first three terms of the Maclaurin series for are A)
B)
C)
D)
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9
Let on the interval The absolute maximum of on this interval is
A)
B)
C)
D)e
on the interval The absolute maximum of on this interval is A)
B)
C)
D)e
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10
What are all values of x for which the series converges?
A)The series converges for only.
B)
C)
D)
converges? A)The series converges for
only.B)
C)
D)
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11
If is a function which is increasing and concave down on the interval ,then which of the following could be the graph of ?
A)
B)
C)
D)
is a function which is increasing and concave down on the interval ,then which of the following could be the graph of ? A)
B)
C)
D)
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12
The tangent line to the curve at intersects the x-axis at
A)
B)
C)-2
D)
at intersects the x-axis at A)
B)
C)-2
D)
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13
A particle moves in the xy-plane such that its velocity vector for time is , .If the particle is at the point when ,then what is the position vector of the particle when ?
A)
B)
C)
D)
is , .If the particle is at the point when ,then what is the position vector of the particle when ? A)
B)
C)
D)
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14
A particle moves in the xy-plane for time according to the parametric equations and .Which of the following statements about the particle are true?
I.
The particle is moving to the right when .
II.
The particle is moving upward when .
III.
The particle is at rest when
A)I only
B)I and II only
C)II and III only
D)I,II,and III
according to the parametric equations and .Which of the following statements about the particle are true? I.
The particle is moving to the right when
.II.
The particle is moving upward when
.III.
The particle is at rest when
A)I only
B)I and II only
C)II and III only
D)I,II,and III
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15
If ,then the slope of the tangent line to at is
A)-21
B)0
C)21
D)undefined
,then the slope of the tangent line to at is A)-21
B)0
C)21
D)undefined
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16
The Maclaurin series represents the function
A)
B)
C)
D)
represents the function A)
B)
C)
D)
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17
The first four terms of the Taylor expansion for about are .What is the value of ?
A)
B)
C)
D)
about are .What is the value of ? A)
B)
C)
D)
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18
Let be the solution to the differential equation .Using Euler's method,starting at the point − with step size ,what is the approximate value of ?
A)8.75
B)-0.75
C)-2.25
D)-1.5
be the solution to the differential equation .Using Euler's method,starting at the point − with step size ,what is the approximate value of ? A)8.75
B)-0.75
C)-2.25
D)-1.5
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19
If y is a function of x such that and ,then
A)
B)
C)
D)
and ,then A)
B)
C)
D)
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20
If ,then
A)
B)
C)
D)
,then A)
B)
C)
D)
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21
If is a function defined on such that ,then which of the following could be the graph of ?
A)
B)
C)
D)
is a function defined on such that ,then which of the following could be the graph of ? A)
B)
C)
D)
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22
Find all values of x in the open interval such that .
such that . Unlock Deck
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23
A particle moves in the xy-plane according to the parametric equations and for .What is the average speed of the particle during the time interval ?
A)7.187
B)6.468
C)7.906
D)6.047
and for .What is the average speed of the particle during the time interval ? A)7.187
B)6.468
C)7.906
D)6.047
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24
The vertical line divides region R into two regions with equal areas.Write,but do not solve,an equation involving integral expressions whose solution gives the value .
divides region R into two regions with equal areas.Write,but do not solve,an equation involving integral expressions whose solution gives the value . Unlock Deck
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25
Which of the following gives the length of the curve over the closed interval
A)
B)
C)
D)
over the closed interval A)
B)
C)
D)
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26
Consider the function defined on the closed interval whose endpoints are and .
Find the absolute maximum of on this interval.Justify your answer.Round your answer to 3 decimals.
Consider the function
defined on the closed interval whose endpoints are and .Find the absolute maximum of
on this interval.Justify your answer.Round your answer to 3 decimals. Unlock Deck
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27
How much water is in Tank 1 after 21 hours? Justify your answer.Round your answer to 3 decimal places.
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28
What is the area enclosed by the lemniscate ?
A)50
B)
C)
D)25
? A)50
B)
C)
D)25
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29
If and ,then
A)
B)
C)
D)
and ,then A)
B)
C)
D)
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30
Oil is pumped continuously from a certain oil well at a rate modeled by the function .Let t be the number of days for a 25-day period and let be measured in barrels per day.To the nearest barrel,according to the model,how much oil will be pumped from the well from the 11th day to the 22nd day?
A)-33,275
B)45,829
C)21,629
D)52,907
.Let t be the number of days for a 25-day period and let be measured in barrels per day.To the nearest barrel,according to the model,how much oil will be pumped from the well from the 11th day to the 22nd day? A)-33,275
B)45,829
C)21,629
D)52,907
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31
A particle moves along the x-axis so that its acceleration is for .If the initial velocity of the particle is 12,then what is the average velocity of the particle during the time interval ?
A)36.955
B)35.045
C)61.045
D)37.045
for .If the initial velocity of the particle is 12,then what is the average velocity of the particle during the time interval ? A)36.955
B)35.045
C)61.045
D)37.045
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32
You may use a calculator for any problem in this section.
Let R be the region enclosed by the graph of and the horizontal line ,as shown in the figure above.
Find the volume of the solid generated when R is rotated about the line .Round your answer to 3 decimal places.
Let R be the region enclosed by the graph of
and the horizontal line ,as shown in the figure above.Find the volume of the solid generated when R is rotated about the line
.Round your answer to 3 decimal places.
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33
What is the average rate at which water flows into Tank 2 for the entire 19-hour period? Justify your answer.Round your answer to 3 decimal places.
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34
A particle moves along the x-axis such that its velocity is given by for time .If the particle has position 15 when ,then what is its position when it comes to rest for the first time?
A)14.889
B)14.188
C)16.094
D)14.594
for time .If the particle has position 15 when ,then what is its position when it comes to rest for the first time? A)14.889
B)14.188
C)16.094
D)14.594
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35
You may use a calculator for any problem in this section.
The rate that water flows into two identical tanks during a 24-hour period is given by the models below.Both and are measured in gallons per hour for hours,and both tanks are empty at time t = 0.
Tank 1: The graph of consists of the line segments indicated in the figure.
Tank 2:
What is the value of ? What is the value of ? Give units for both answers.Round your answer to 3 decimal places.
___________
___________
The rate that water flows into two identical tanks during a 24-hour period is given by the models below.Both
and are measured in gallons per hour for hours,and both tanks are empty at time t = 0.Tank 1: The graph of
consists of the line segments indicated in the figure.Tank 2:
What is the value of
? What is the value of ? Give units for both answers.Round your answer to 3 decimal places.
___________
___________ Unlock Deck
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36
What is the value of .
A)
B)
C)
D)Does not exist
. A)
B)
C)
D)Does not exist
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37
Let .If represents the nth derivative of ,then what is ?
A)
B)
C)
D)
.If represents the nth derivative of ,then what is ? A)
B)
C)
D)
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38
For the function , .If is the inverse of ,what is the slope of the tangent to at the point ?
A)0.276
B)0.226
C)0.251
D)0.211
, .If is the inverse of ,what is the slope of the tangent to at the point ? A)0.276
B)0.226
C)0.251
D)0.211
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39
During the 24-hour period,is there ever a time other than when the amount of water in the two tanks is the same? If yes,find all such values of .If no,explain why not.If needed,round your answer to 3 decimal places.
when the amount of water in the two tanks is the same? If yes,find all such values of .If no,explain why not.If needed,round your answer to 3 decimal places. Unlock Deck
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40
Region R is the base of a solid.For this solid,each cross section perpendicular to the x-axis is a rectangle whose height is twice as long as the length in R.Find the volume of the solid.Round your answer to 3 decimal.
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41
The graph of is pictured below.Which of the following statements about are true?
i.A left endpoint approximation is greater than .II.A right endpoint approximation is less than .III.A trapezoidal approximation is less than
A)None are true
B)III only
C)I and III only
D)I,II,and III
is pictured below.Which of the following statements about are true? i.A left endpoint approximation is greater than
.II.A right endpoint approximation is less than .III.A trapezoidal approximation is less than A)None are true
B)III only
C)I and III only
D)I,II,and III
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42
Let .
Find all values of for which converges.
Let
.Find all values of
for which converges. Unlock Deck
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43
The equation of the tangent line to the function at is
A)
B)
C)
D)
at is A)
B)
C)
D)
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44
Use the values to sketch a slope field for on the axes provided.
A)
B)
C)
D)
on the axes provided. A)
B)
C)
D)
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45
Use the first three terms of to estimate the value of .Round your answer to 3 decimal places.
to estimate the value of .Round your answer to 3 decimal places. Unlock Deck
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46
A particle moves in the xy-plane with position for all real values of given by the parametric equations and .
Give the coordinates of the velocity vector for any time .
given by the parametric equations and .Give the coordinates of the velocity vector for any time
. Unlock Deck
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47
Consider the differential equation ,where is the solution to the equation and .Using Euler's method starting at with step size ,what is the approximation for ?
A)-3.5
B)-3
C)-2.5
D)-2
,where is the solution to the equation and .Using Euler's method starting at with step size ,what is the approximation for ? A)-3.5
B)-3
C)-2.5
D)-2
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48
Give the coordinates of the acceleration vector at a time when the particle is at rest.
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49
Is the particle moving to the left or right when ? Is the particle moving up or down when ?
A)left and up
B)left and down
C)right and up
D)right and down
? Is the particle moving up or down when ? A)left and up
B)left and down
C)right and up
D)right and down
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50
Determine the point(s)of inflection for .
. Unlock Deck
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51
How fast is the particle moving when its horizontal position is
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52
Evaluate .
A)0
B)1
C)2e
D)∞
. A)0
B)1
C)2e
D)∞
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53
The position vector for a particle moving in the -plane for is 1st The slope of the tangent line to the path of the particle at is
A)
B)
C)
D)162.5
-plane for is 1st The slope of the tangent line to the path of the particle at is A)
B)
C)
D)162.5
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54
If ,then
A)
B)
C)
D)
,then A)
B)
C)
D)
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55
What is the slope of the path of the particle when ?
? Unlock Deck
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56
Show that is a solution to the differential equation .
is a solution to the differential equation . Unlock Deck
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57
Find the particular solution .
. Unlock Deck
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58
Find the limit .
A)0
B)
C)
D)∞
. A)0
B)
C)
D)∞
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59
Using Euler's method starting at with step size ,estimate the value of .
with step size ,estimate the value of .
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60
If is a function such that is increasing for and is decreasing for ,then which of the following could be the graph of ?
A)
B)
C)
D)
is a function such that is increasing for and is decreasing for ,then which of the following could be the graph of ? A)
B)
C)
D)
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61
Which of the following series converge?
i. II. III.
A)I only
B)I and II
C)I and III
D)I,II,and III
i.
II. III. A)I only
B)I and II
C)I and III
D)I,II,and III
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62
If and ,then
A)
B)
C)
D)
and ,then A)
B)
C)
D)
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63
The acceleration vector of a particle moving in the -plane is ,for .If the velocity vector at is ,then how fast is the particle moving when ?
A)5
B)6
C)
D)
-plane is ,for .If the velocity vector at is ,then how fast is the particle moving when ? A)5
B)6
C)
D)
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64
The graph of has inflection points at
A)- and
only.
B)0 and only.
C)0 and only.
D)- ,0 and
.
has inflection points at A)-
and only.B)0 and
only.C)0 and
only.D)-
,0 and . Unlock Deck
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65
If ,then
A)
B)
C)
D)
,then A)
B)
C)
D)
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66
What are all the values of for which the series converges?
A)
B)
C)
D)
for which the series converges? A)
B)
C)
D)
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67
The graph of below,consisting of a pair of line segments,is pictured below.
If ,then
A)3
B)4
C)4.5
D)5.5
below,consisting of a pair of line segments,is pictured below. If
,then A)3
B)4
C)4.5
D)5.5
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68
Let ,where is pictured above.
What is the domain of ?
A)All real numbers except -1 and 5
B)
C)
D)
Let
,where is pictured above.
What is the domain of
? A)All real numbers except -1 and 5
B)
C)
D)
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69
The volume of the solid generated by revolving the region enclosed between the graph of and the lines and about the -axis is given by which integral expression?
A)
B)
C)
D)
and the lines and about the -axis is given by which integral expression? A)
B)
C)
D)
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70
The area enclosed by the polar curve in the interval is
A)
B)
C)
D)
in the interval is A)
B)
C)
D)
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71
A particle moves in the -plane according to the parametric equations and .An expression for the length of the path of the particle from to is
A)
B)
C)
D)
-plane according to the parametric equations and .An expression for the length of the path of the particle from to is A)
B)
C)
D)
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72
The general solution to the differential equation is
A)
B)
C)
D)
is A)
B)
C)
D)
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73
Evaluate the limit,if it exists: .
A)0
B)1
C)-1
D)The limit does not exist
. A)0
B)1
C)-1
D)The limit does not exist
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74
The first four terms of the Taylor expansion for about are .What is the value of ?
A)- 6
B)- 3
C)-
D)-
about are .What is the value of ? A)- 6
B)- 3
C)-
D)-
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75
Let .The first four nonzero terms of the Taylor approximation for about are
A)
B)
C)
D)
.The first four nonzero terms of the Taylor approximation for about are A)
B)
C)
D)
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76
What is the slope of the curve at the point ?
A)
B)
C)
D)
at the point ? A)
B)
C)
D)
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77
The slope field at the bottom represents an approximation to the general solution to which differential equation?
A)
B)
C)
D)
A)
B)
C)
D)
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78
What is the value of ?
A)0
B)1
C)2
D)4
? A)0
B)1
C)2
D)4
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79
The slope of the normal line to at is
A)
B)0
C)
D)10
at is A)
B)0
C)
D)10
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80
Which expression below represents the first four terms of the Maclaurin approximation to the area under the curve from to ?
A)
B)
C)
D)
from to ? A)
B)
C)
D)
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