تكلم مع الذكاء الاصطناعي
Deck 9: Further Applications of the Integral and Taylor Polynomials
ملء الشاشة (f)
سؤال
Approximate the arc length of the curve 
over the interval 
using Simpson's Rule 
.
over the interval using Simpson's Rule .
سؤال
Let 
be the solid obtained by revolving the infinite graph of 
about the x-axis for 
. 
Which of the following statements is correct?
A)
has infinite volume and finite surface area.
B)
has finite volume and infinite surface area.
C)
has finite volume and finite surface area.
D)
has infinite volume and infinite surface area.
E) None of the above is correct.
be the solid obtained by revolving the infinite graph of about the x-axis for . Which of the following statements is correct?A)
has infinite volume and finite surface area.B)
has finite volume and infinite surface area.C)
has finite volume and finite surface area.D)
has infinite volume and infinite surface area.E) None of the above is correct.
سؤال
Approximate the arc length of the curve 
over the interval 
using the Trapezoidal Rule 
.
over the interval using the Trapezoidal Rule . سؤال
Compute the surface area of revolution of 
about the x-axis over the interval 
.
about the x-axis over the interval . سؤال
Calculate the arc length of 
over the interval 
.
over the interval . سؤال
Calculate the arc length of the curve 
over the interval 
.
over the interval . سؤال
Compute the area of the surface obtained by rotating the graph of 
, 
about the x-axis. 
, about the x-axis. سؤال
Compute the surface area of revolution of 
about the x-axis over the interval 
.
about the x-axis over the interval . سؤال
Compute the surface area of revolution of 
about the x-axis over the interval 
.
about the x-axis over the interval . سؤال
Calculate the arc length of the curve 
over the interval 
.
over the interval . سؤال
Compute the arc length of 
for 
.
for . سؤال
Compute the surface area of revolution of 
about the x-axis over the interval 
.
about the x-axis over the interval . سؤال
Use implicit differentiation to compute the surface area of revolution about the x-axis of the part of the astroid 
in the first quadrant. 
in the first quadrant. سؤال
Find the area of the surface obtained by rotating the graph of 
, 
about the x-axis. 
, about the x-axis. سؤال
Calculate the arc length of ![Calculate the arc length of over the interval [1, 5].<div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB5596/11eaa655_3af6_1d21_a696_970bec6b9115_TB5596_11.jpg)
over the interval [1, 5].
over the interval [1, 5]. سؤال
Let 
be the solid obtained by revolving the infinite graph of 
about the x-axis for 
. 
Which of the following statements is correct?
A)
has finite volume and finite surface area.
B)
has finite surface area and infinite volume.
C)
has finite volume and infinite surface area.
D)
has infinite volume and infinite surface area.
E) None of the above is correct.
be the solid obtained by revolving the infinite graph of about the x-axis for . Which of the following statements is correct?A)
has finite volume and finite surface area.B)
has finite surface area and infinite volume.C)
has finite volume and infinite surface area.D)
has infinite volume and infinite surface area.E) None of the above is correct.
سؤال
Compute the surface area of revolution of 
about the x-axis over the interval 
.
about the x-axis over the interval . سؤال
Compute the arc length of ![Compute the arc length of over the interval [0, 2].<div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB5596/11eaa655_3af6_6a4a_a696_81853635175a_TB5596_11.jpg)
over the interval [0, 2].
over the interval [0, 2]. سؤال
Find the area of the surface obtained by rotating the loop 
, 
, 
about the x-axis.
Use implicit differentiation to facilitate your computations.
, , about the x-axis.Use implicit differentiation to facilitate your computations.
سؤال
Calculate the arc length of 
over the interval 
.
over the interval . سؤال
The plate shown in the figure, determined by the region enclosed by the graphs of 
, 
, and 
, is submerged vertically in a fluid with density 
so that its top edge is level with the surface of the fluid. Find the force on a side of the plate if 
is given in terms of weight per unit volume. 
, , and , is submerged vertically in a fluid with density so that its top edge is level with the surface of the fluid. Find the force on a side of the plate if is given in terms of weight per unit volume. سؤال
The face of a dam is an isosceles trapezoid of height 30 ft and bases 10 ft and 50 ft. The dam is oriented vertically with the larger base at the bottom. Find the force on the dam if the water level is 4 ft below the top of the dam. (The density of the water is 
.) 
.) سؤال
The plate shown in the figure is submerged in water so that its top is level with the surface of the water. Find the fluid pressure on a side of the plate. (The density of water is 
.) 
.) سؤال
An infinite plate shown in the figure below, bounded by the graphs of 
and 
and the y-axis, is submerged vertically in water, with its top 
ft below the water surface.
Calculate the fluid force on a side of the plate. (The density of water is
) 
and and the y-axis, is submerged vertically in water, with its top ft below the water surface.Calculate the fluid force on a side of the plate. (The density of water is
) سؤال
The plate shown in the figure, enclosed by the curves 
, 
, and 
, is submerged vertically in a fluid with density 
so that its top is at a depth of 
. Find the fluid pressure on a side of the plate if 
is given in terms of weight per unit volume. 
, , and , is submerged vertically in a fluid with density so that its top is at a depth of . Find the fluid pressure on a side of the plate if is given in terms of weight per unit volume. سؤال
An infinite plate shown in the figure below, bounded by the graphs of 
and 
and the y-axis, is submerged vertically in water, with its top 
ft below the water surface.
Calculate the fluid force on a side of the plate. (The density of water is
) 
and and the y-axis, is submerged vertically in water, with its top ft below the water surface.Calculate the fluid force on a side of the plate. (The density of water is
) سؤال
A thin plate shown in the figure below, bounded by the curves 
, 
, and 
is submerged vertically in water, with its top level with the water's surface. Calculate the fluid force on a side of the plate.
(The density of water is
) 
, , and is submerged vertically in water, with its top level with the water's surface. Calculate the fluid force on a side of the plate.(The density of water is
) سؤال
Calculate the arc length of 
over the interval 
over the interval سؤال
A water tank is a cylinder 4 ft in diameter, standing on its base. If water fills the tank to a depth of 3 ft, what is the magnitude of the force exerted on the side of the tank? (The density of the water is 
.) 
.) سؤال
An infinite plate shown in the figure below, bounded by the graphs of 
and 
and the two axes, is submerged vertically in a fluid with density 
in kilograms per cubic meter; its top is level with the fluid surface.
Calculate the fluid force on a side of the plate and write the answer in terms of
and 
. 
and and the two axes, is submerged vertically in a fluid with density in kilograms per cubic meter; its top is level with the fluid surface.Calculate the fluid force on a side of the plate and write the answer in terms of
and . سؤال
The plate shown in the figure below, bounded by the graph of 
and the
y-axis, is submerged vertically in a fluid with density
so that its top is level with the fluid surface.
Find the fluid pressure on a side of the plate if
is given in terms of weight per unit volume. 
and they-axis, is submerged vertically in a fluid with density
so that its top is level with the fluid surface.Find the fluid pressure on a side of the plate if
is given in terms of weight per unit volume. سؤال
The plate determined by the region between the graphs of 
and 
is submerged in a fluid with density 
, with its top touching the surface of the fluid.
Find the fluid pressure on a side of the plate if
is given in terms of weight per unit volume. 
and is submerged in a fluid with density , with its top touching the surface of the fluid.Find the fluid pressure on a side of the plate if
is given in terms of weight per unit volume. سؤال
Compute the arc length of 
for 
.
for . سؤال
A thin plate shown in the figure, bounded by the graphs 
and 
and the x-axis, is submerged vertically in a fluid of density 
so that its top is level with the fluid surface.
Calculate the fluid pressure on a side of the plate if
is given in terms of weight per unit volume. 
and and the x-axis, is submerged vertically in a fluid of density so that its top is level with the fluid surface.Calculate the fluid pressure on a side of the plate if
is given in terms of weight per unit volume. سؤال
An infinite plate shown in the figure below, bounded by the graphs of 
, 
, and the y-axis, is submerged vertically in water, with its top 
ft below the water surface. Calculate the fluid force on a side of the plate.
(The density of water is
) 
, , and the y-axis, is submerged vertically in water, with its top ft below the water surface. Calculate the fluid force on a side of the plate.(The density of water is
) سؤال
Approximate the arc length of the curve 
over the interval 
using Simpson's Rule 
.
over the interval using Simpson's Rule . سؤال
Find the surface area of the ellipsoid obtained by rotating the ellipse 
about the x-axis.
about the x-axis. سؤال
A thin plate shown in the following figure is bounded by the graphs of 
and 
. The plate is submerged in a fluid with density 
so that its top is level with the surface of the fluid.
Calculate the fluid pressure on a side of the plate if
is given in terms of weight per unit volume. 
and . The plate is submerged in a fluid with density so that its top is level with the surface of the fluid.Calculate the fluid pressure on a side of the plate if
is given in terms of weight per unit volume. سؤال
Let 
be the region shown in the figure below enclosed by the graph of 
,
the positive x-axis, and the negative y-axis.
Calculate the fluid force on a side of the plate in the shape
if the water surface is at 
.
(The density of water is w =
) 
be the region shown in the figure below enclosed by the graph of ,the positive x-axis, and the negative y-axis.
Calculate the fluid force on a side of the plate in the shape
if the water surface is at .(The density of water is w =
) سؤال
A thin plate shown in the figure below, bounded by the curves 
and 
, is submerged vertically in water with its top 
ft below the water surface. Calculate the fluid force on a side of the plate.
(The density of water is
) 
and , is submerged vertically in water with its top ft below the water surface. Calculate the fluid force on a side of the plate.(The density of water is
) سؤال
A right triangle is submerged vertically in water so that the base is the part of the triangle which is closest to the surface. Suppose that the base of the triangle is 2 ft long, and the height is 6 ft. What is the fluid force on a side of the triangle if the base is 3 ft from the surface? (The density of water is 
)
) سؤال
Find the center of mass of the region enclosed by the graphs of 
and 
. 
and . سؤال
Find the centroid of the shaded region in the following figure. 
سؤال
An infinite plate occupying the region bounded by the functions 
and 
on the interval 
is submerged vertically so that the top of the plate is under 1.5 m of water. What is the fluid force on the side of the plate?
and on the interval is submerged vertically so that the top of the plate is under 1.5 m of water. What is the fluid force on the side of the plate? سؤال
سؤال
Find the centroid of the quarter ring shown in the figure below. 
سؤال
Find the centroid of the shaded region in the figure below. 
سؤال
Find the centroid of the region enclosed by the curves 
and 
. 
and . سؤال
A plate bounded by the functions 
and 
on the interval 
is submerged vertically so that the top of the plate is under 1 m of water. What is the fluid force on the side of the plate?
and on the interval is submerged vertically so that the top of the plate is under 1 m of water. What is the fluid force on the side of the plate? سؤال
A plate occupying the region bounded by the functions 
and 
is submerged vertically so that the top of the plate is under 2 m of water. What is the fluid force on the side of the plate?
and is submerged vertically so that the top of the plate is under 2 m of water. What is the fluid force on the side of the plate? سؤال
A plate bounded by the functions 
, 
, 
and 
is submerged vertically so that the top of the plate is under 4 m of water. What is the fluid force on the side of the plate?
, , and is submerged vertically so that the top of the plate is under 4 m of water. What is the fluid force on the side of the plate? سؤال
Use additivity of moments to find the center of mass of the region consisting of a semicircle on top of an isosceles trapezoid of height 1 and bases 2 and 4, as shown below. 
سؤال
Find the centroid of the region in the figure below enclosed by the circle 
and the two tangents to the circle intersecting at the point 
. 
and the two tangents to the circle intersecting at the point . سؤال
Find the centroid of the region lying between the graphs of 
and 
over the interval 
. 
and over the interval . سؤال
The centroid of the region enclosed by the graphs of 
and 
lies on the line
A)
B)
C)
D)
E)
and lies on the lineA)
B)
C)
D)
E)
سؤال
Let 
be an invertible function such that 
and 
. Let 
be the region enclosed by the graphs of 
and 
over the interval 
. The centroid of 
lies on
A) the line
.
B) the line
.
C) the line
.
D) It depends on the function
.
E) none of the above.
be an invertible function such that and . Let be the region enclosed by the graphs of and over the interval . The centroid of lies onA) the line
.B) the line
.C) the line
.D) It depends on the function
.E) none of the above.
سؤال
A water tank is a rectangular tank with a square base of side length 4 ft and a height of 3 ft, standing on its base. If oil fills the tank to a depth of 2 ft, what is the magnitude of the force exerted on each of the vertical sides of the tank? (The density of the oil is 
.)
.) سؤال
A plate occupying the region bounded by the functions 
and 
is submerged vertically so that the top of the plate is under 2 m of water. What is the fluid force on the side of the plate?
and is submerged vertically so that the top of the plate is under 2 m of water. What is the fluid force on the side of the plate? سؤال
A plate occupying the region bounded by the functions 
and 
is submerged vertically so that the top of the plate is under 5 m of water. What is the fluid force on the side of the plate?
and is submerged vertically so that the top of the plate is under 5 m of water. What is the fluid force on the side of the plate? سؤال
Find the centroid of the shaded region in the figure below. 
سؤال
Find the center of mass of the region enclosed by the graphs of 
and 
. 
and . سؤال
Calculate the Taylor polynomial 
centered at 
for 
.
centered at for . سؤال
Find the centroid of the region enclosed by the graphs 
, 
, 
, and 
, , , and سؤال
The quotient 
is equal to:
A)
where 
B)
where 
C)
where 
D)
where 
E) none of the above.
is equal to:A)
where B)
where C)
where D)
where E) none of the above.
سؤال
Let 
be the Taylor polynomial of 
centered at 
. Which of the following statements is correct?
A)
B)
C)
D)
E) None of the above is correct.
be the Taylor polynomial of centered at . Which of the following statements is correct?A)
B)
C)
D)
E) None of the above is correct.
سؤال
Compute 
for 
centered at 
. Use the error bound to find the maximum possible size of error of 
.
for centered at . Use the error bound to find the maximum possible size of error of . سؤال
Compute 
for 
centered at 
. Use the error bound to find the maximum possible size of error of 
.
for centered at . Use the error bound to find the maximum possible size of error of . سؤال
Which of the following is a Maclaurin polynomial of 
?
A)
B)
C)
D)
E)
?A)
B)
C)
D)
E)
سؤال
سؤال
Find the centroid of the region enclosed by the graph of 
, the tangent to the graph at 
and the y-axis. 
, the tangent to the graph at and the y-axis. سؤال
Five particles of equal mass are located at 
and 
. Find the center of mass of the system.
and . Find the center of mass of the system. سؤال
Find the centroid of the shaded region in the figure below. 
سؤال
In the following figure, the centroid of the region enclosed by the graphs of 
, 
and 
lies on: 
A) the line
B) the line
C) the line
D) the graph of
E) the graph of
, and lies on: A) the line
B) the line
C) the line
D) the graph of
E) the graph of
سؤال
Find 
for the lamina of uniform density 
occupying the region under 
from 
.
for the lamina of uniform density occupying the region under from . سؤال
Find the centroid of the shaded region shown in the figure below. 
سؤال
Calculate the Maclaurin polynomial 
for 
.
for . سؤال
Which of the following are Maclaurin polynomials of 
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
سؤال
The centroid of the region shown in the figure below enclosed by the graphs of 
, 
, and 
lies on: 
A) the line
B) the line
C) the line
D) the graph of
E) the graph of
, , and lies on: A) the line
B) the line
C) the line
D) the graph of
E) the graph of
سؤال
Four particles with masses of 4, 5, 7, and 3 are located respectively at 
and 
. Find 
such that the center of mass of the system is located at the point 
.
and . Find such that the center of mass of the system is located at the point . سؤال
Calculate the Maclaurin polynomial 
for 
.
for .
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ملء الشاشة (f)
Deck 9: Further Applications of the Integral and Taylor Polynomials
1
Approximate the arc length of the curve over the interval using Simpson's Rule .
over the interval using Simpson's Rule .4.27
2
Let be the solid obtained by revolving the infinite graph of about the x-axis for . Which of the following statements is correct?
A) has infinite volume and finite surface area.
B) has finite volume and infinite surface area.
C) has finite volume and finite surface area.
D) has infinite volume and infinite surface area.
E) None of the above is correct.
be the solid obtained by revolving the infinite graph of about the x-axis for . Which of the following statements is correct?A)
has infinite volume and finite surface area.B)
has finite volume and infinite surface area.C)
has finite volume and finite surface area.D)
has infinite volume and infinite surface area.E) None of the above is correct.
has finite volume and infinite surface area. 3
Approximate the arc length of the curve over the interval using the Trapezoidal Rule .
over the interval using the Trapezoidal Rule .21.956
4
Compute the surface area of revolution of about the x-axis over the interval .
about the x-axis over the interval . فتح الحزمة
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5
Calculate the arc length of over the interval .
over the interval . فتح الحزمة
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6
Calculate the arc length of the curve over the interval .
over the interval . فتح الحزمة
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7
Compute the area of the surface obtained by rotating the graph of , about the x-axis.
, about the x-axis. فتح الحزمة
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8
Compute the surface area of revolution of about the x-axis over the interval .
about the x-axis over the interval . فتح الحزمة
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9
Compute the surface area of revolution of about the x-axis over the interval .
about the x-axis over the interval . فتح الحزمة
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10
Calculate the arc length of the curve over the interval .
over the interval . فتح الحزمة
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11
Compute the arc length of for .
for . فتح الحزمة
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12
Compute the surface area of revolution of about the x-axis over the interval .
about the x-axis over the interval . فتح الحزمة
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13
Use implicit differentiation to compute the surface area of revolution about the x-axis of the part of the astroid in the first quadrant.
in the first quadrant. فتح الحزمة
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14
Find the area of the surface obtained by rotating the graph of , about the x-axis.
, about the x-axis. فتح الحزمة
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15
Calculate the arc length of over the interval [1, 5].
over the interval [1, 5]. فتح الحزمة
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16
Let be the solid obtained by revolving the infinite graph of about the x-axis for . Which of the following statements is correct?
A) has finite volume and finite surface area.
B) has finite surface area and infinite volume.
C) has finite volume and infinite surface area.
D) has infinite volume and infinite surface area.
E) None of the above is correct.
be the solid obtained by revolving the infinite graph of about the x-axis for . Which of the following statements is correct?A)
has finite volume and finite surface area.B)
has finite surface area and infinite volume.C)
has finite volume and infinite surface area.D)
has infinite volume and infinite surface area.E) None of the above is correct.
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17
Compute the surface area of revolution of about the x-axis over the interval .
about the x-axis over the interval . فتح الحزمة
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18
Compute the arc length of over the interval [0, 2].
over the interval [0, 2]. فتح الحزمة
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19
Find the area of the surface obtained by rotating the loop , , about the x-axis.
Use implicit differentiation to facilitate your computations.
, , about the x-axis.Use implicit differentiation to facilitate your computations.
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20
Calculate the arc length of over the interval .
over the interval . فتح الحزمة
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21
The plate shown in the figure, determined by the region enclosed by the graphs of , , and , is submerged vertically in a fluid with density so that its top edge is level with the surface of the fluid. Find the force on a side of the plate if is given in terms of weight per unit volume.
, , and , is submerged vertically in a fluid with density so that its top edge is level with the surface of the fluid. Find the force on a side of the plate if is given in terms of weight per unit volume. فتح الحزمة
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22
The face of a dam is an isosceles trapezoid of height 30 ft and bases 10 ft and 50 ft. The dam is oriented vertically with the larger base at the bottom. Find the force on the dam if the water level is 4 ft below the top of the dam. (The density of the water is .)
.) فتح الحزمة
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23
The plate shown in the figure is submerged in water so that its top is level with the surface of the water. Find the fluid pressure on a side of the plate. (The density of water is .)
.) فتح الحزمة
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24
An infinite plate shown in the figure below, bounded by the graphs of and and the y-axis, is submerged vertically in water, with its top ft below the water surface.
Calculate the fluid force on a side of the plate. (The density of water is )
and and the y-axis, is submerged vertically in water, with its top ft below the water surface.Calculate the fluid force on a side of the plate. (The density of water is
) فتح الحزمة
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25
The plate shown in the figure, enclosed by the curves , , and , is submerged vertically in a fluid with density so that its top is at a depth of . Find the fluid pressure on a side of the plate if is given in terms of weight per unit volume.
, , and , is submerged vertically in a fluid with density so that its top is at a depth of . Find the fluid pressure on a side of the plate if is given in terms of weight per unit volume. فتح الحزمة
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26
An infinite plate shown in the figure below, bounded by the graphs of and and the y-axis, is submerged vertically in water, with its top ft below the water surface.
Calculate the fluid force on a side of the plate. (The density of water is )
and and the y-axis, is submerged vertically in water, with its top ft below the water surface.Calculate the fluid force on a side of the plate. (The density of water is
) فتح الحزمة
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27
A thin plate shown in the figure below, bounded by the curves , , and is submerged vertically in water, with its top level with the water's surface. Calculate the fluid force on a side of the plate.
(The density of water is )
, , and is submerged vertically in water, with its top level with the water's surface. Calculate the fluid force on a side of the plate.(The density of water is
) فتح الحزمة
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28
Calculate the arc length of over the interval
over the interval فتح الحزمة
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29
A water tank is a cylinder 4 ft in diameter, standing on its base. If water fills the tank to a depth of 3 ft, what is the magnitude of the force exerted on the side of the tank? (The density of the water is .)
.) فتح الحزمة
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30
An infinite plate shown in the figure below, bounded by the graphs of and and the two axes, is submerged vertically in a fluid with density in kilograms per cubic meter; its top is level with the fluid surface.
Calculate the fluid force on a side of the plate and write the answer in terms of and .
and and the two axes, is submerged vertically in a fluid with density in kilograms per cubic meter; its top is level with the fluid surface.Calculate the fluid force on a side of the plate and write the answer in terms of
and . فتح الحزمة
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31
The plate shown in the figure below, bounded by the graph of and the
y-axis, is submerged vertically in a fluid with density so that its top is level with the fluid surface.
Find the fluid pressure on a side of the plate if is given in terms of weight per unit volume.
and they-axis, is submerged vertically in a fluid with density
so that its top is level with the fluid surface.Find the fluid pressure on a side of the plate if
is given in terms of weight per unit volume. فتح الحزمة
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32
The plate determined by the region between the graphs of and is submerged in a fluid with density , with its top touching the surface of the fluid.
Find the fluid pressure on a side of the plate if is given in terms of weight per unit volume.
and is submerged in a fluid with density , with its top touching the surface of the fluid.Find the fluid pressure on a side of the plate if
is given in terms of weight per unit volume. فتح الحزمة
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33
Compute the arc length of for .
for . فتح الحزمة
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34
A thin plate shown in the figure, bounded by the graphs and and the x-axis, is submerged vertically in a fluid of density so that its top is level with the fluid surface.
Calculate the fluid pressure on a side of the plate if is given in terms of weight per unit volume.
and and the x-axis, is submerged vertically in a fluid of density so that its top is level with the fluid surface.Calculate the fluid pressure on a side of the plate if
is given in terms of weight per unit volume. فتح الحزمة
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35
An infinite plate shown in the figure below, bounded by the graphs of , , and the y-axis, is submerged vertically in water, with its top ft below the water surface. Calculate the fluid force on a side of the plate.
(The density of water is )
, , and the y-axis, is submerged vertically in water, with its top ft below the water surface. Calculate the fluid force on a side of the plate.(The density of water is
) فتح الحزمة
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36
Approximate the arc length of the curve over the interval using Simpson's Rule .
over the interval using Simpson's Rule . فتح الحزمة
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37
Find the surface area of the ellipsoid obtained by rotating the ellipse about the x-axis.
about the x-axis. فتح الحزمة
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38
A thin plate shown in the following figure is bounded by the graphs of and . The plate is submerged in a fluid with density so that its top is level with the surface of the fluid.
Calculate the fluid pressure on a side of the plate if is given in terms of weight per unit volume.
and . The plate is submerged in a fluid with density so that its top is level with the surface of the fluid.Calculate the fluid pressure on a side of the plate if
is given in terms of weight per unit volume. فتح الحزمة
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39
Let be the region shown in the figure below enclosed by the graph of ,
the positive x-axis, and the negative y-axis.
Calculate the fluid force on a side of the plate in the shape if the water surface is at .
(The density of water is w = )
be the region shown in the figure below enclosed by the graph of ,the positive x-axis, and the negative y-axis.
Calculate the fluid force on a side of the plate in the shape
if the water surface is at .(The density of water is w =
) فتح الحزمة
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40
A thin plate shown in the figure below, bounded by the curves and , is submerged vertically in water with its top ft below the water surface. Calculate the fluid force on a side of the plate.
(The density of water is )
and , is submerged vertically in water with its top ft below the water surface. Calculate the fluid force on a side of the plate.(The density of water is
) فتح الحزمة
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41
A right triangle is submerged vertically in water so that the base is the part of the triangle which is closest to the surface. Suppose that the base of the triangle is 2 ft long, and the height is 6 ft. What is the fluid force on a side of the triangle if the base is 3 ft from the surface? (The density of water is )
) فتح الحزمة
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42
Find the center of mass of the region enclosed by the graphs of and .
and . فتح الحزمة
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43
Find the centroid of the shaded region in the following figure.
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44
An infinite plate occupying the region bounded by the functions and on the interval is submerged vertically so that the top of the plate is under 1.5 m of water. What is the fluid force on the side of the plate?
and on the interval is submerged vertically so that the top of the plate is under 1.5 m of water. What is the fluid force on the side of the plate? فتح الحزمة
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45
A rectangular box with height 2 m, width 3 m, and length 4 m is submerged in a pool of water. The top of the box is 5 m below the surface of the water.
Compute the fluid force on one of the box sides with dimensions 4 m by 2 m.
Compute the fluid force on one of the box sides with dimensions 4 m by 2 m.
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46
Find the centroid of the quarter ring shown in the figure below.
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47
Find the centroid of the shaded region in the figure below.
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48
Find the centroid of the region enclosed by the curves and .
and . فتح الحزمة
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49
A plate bounded by the functions and on the interval is submerged vertically so that the top of the plate is under 1 m of water. What is the fluid force on the side of the plate?
and on the interval is submerged vertically so that the top of the plate is under 1 m of water. What is the fluid force on the side of the plate? فتح الحزمة
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50
A plate occupying the region bounded by the functions and is submerged vertically so that the top of the plate is under 2 m of water. What is the fluid force on the side of the plate?
and is submerged vertically so that the top of the plate is under 2 m of water. What is the fluid force on the side of the plate? فتح الحزمة
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51
A plate bounded by the functions , , and is submerged vertically so that the top of the plate is under 4 m of water. What is the fluid force on the side of the plate?
, , and is submerged vertically so that the top of the plate is under 4 m of water. What is the fluid force on the side of the plate? فتح الحزمة
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52
Use additivity of moments to find the center of mass of the region consisting of a semicircle on top of an isosceles trapezoid of height 1 and bases 2 and 4, as shown below.
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53
Find the centroid of the region in the figure below enclosed by the circle and the two tangents to the circle intersecting at the point .
and the two tangents to the circle intersecting at the point . فتح الحزمة
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54
Find the centroid of the region lying between the graphs of and over the interval .
and over the interval . فتح الحزمة
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55
The centroid of the region enclosed by the graphs of and lies on the line
A)
B)
C)
D)
E)
and lies on the lineA)
B)
C)
D)
E)
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56
Let be an invertible function such that and . Let be the region enclosed by the graphs of and over the interval . The centroid of lies on
A) the line .
B) the line .
C) the line .
D) It depends on the function .
E) none of the above.
be an invertible function such that and . Let be the region enclosed by the graphs of and over the interval . The centroid of lies onA) the line
.B) the line
.C) the line
.D) It depends on the function
.E) none of the above.
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57
A water tank is a rectangular tank with a square base of side length 4 ft and a height of 3 ft, standing on its base. If oil fills the tank to a depth of 2 ft, what is the magnitude of the force exerted on each of the vertical sides of the tank? (The density of the oil is .)
.) فتح الحزمة
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58
A plate occupying the region bounded by the functions and is submerged vertically so that the top of the plate is under 2 m of water. What is the fluid force on the side of the plate?
and is submerged vertically so that the top of the plate is under 2 m of water. What is the fluid force on the side of the plate? فتح الحزمة
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59
A plate occupying the region bounded by the functions and is submerged vertically so that the top of the plate is under 5 m of water. What is the fluid force on the side of the plate?
and is submerged vertically so that the top of the plate is under 5 m of water. What is the fluid force on the side of the plate? فتح الحزمة
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60
Find the centroid of the shaded region in the figure below.
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61
Find the center of mass of the region enclosed by the graphs of and .
and . فتح الحزمة
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62
Calculate the Taylor polynomial centered at for .
centered at for . فتح الحزمة
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63
Find the centroid of the region enclosed by the graphs , , , and
, , , and فتح الحزمة
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64
The quotient is equal to:
A) where
B) where
C) where
D) where
E) none of the above.
is equal to:A)
where B)
where C)
where D)
where E) none of the above.
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65
Let be the Taylor polynomial of centered at . Which of the following statements is correct?
A)
B)
C)
D)
E) None of the above is correct.
be the Taylor polynomial of centered at . Which of the following statements is correct?A)
B)
C)
D)
E) None of the above is correct.
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66
Compute for centered at . Use the error bound to find the maximum possible size of error of .
for centered at . Use the error bound to find the maximum possible size of error of . فتح الحزمة
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67
Compute for centered at . Use the error bound to find the maximum possible size of error of .
for centered at . Use the error bound to find the maximum possible size of error of . فتح الحزمة
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68
Which of the following is a Maclaurin polynomial of ?
A)
B)
C)
D)
E)
?A)
B)
C)
D)
E)
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69
Find the centroid of the portion of the unit circle lying within the first three quadrants.
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70
Find the centroid of the region enclosed by the graph of , the tangent to the graph at and the y-axis.
, the tangent to the graph at and the y-axis. فتح الحزمة
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71
Five particles of equal mass are located at and . Find the center of mass of the system.
and . Find the center of mass of the system. فتح الحزمة
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72
Find the centroid of the shaded region in the figure below.
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73
In the following figure, the centroid of the region enclosed by the graphs of , and lies on:
A) the line
B) the line
C) the line
D) the graph of
E) the graph of
, and lies on: A) the line
B) the line
C) the line
D) the graph of
E) the graph of
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74
Find for the lamina of uniform density occupying the region under from .
for the lamina of uniform density occupying the region under from . فتح الحزمة
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75
Find the centroid of the shaded region shown in the figure below.
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76
Calculate the Maclaurin polynomial for .
for . فتح الحزمة
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77
Which of the following are Maclaurin polynomials of
A)
B)
C)
D)
E)
A)
B)
C)
D)
E)
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78
The centroid of the region shown in the figure below enclosed by the graphs of , , and lies on:
A) the line
B) the line
C) the line
D) the graph of
E) the graph of
, , and lies on: A) the line
B) the line
C) the line
D) the graph of
E) the graph of
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79
Four particles with masses of 4, 5, 7, and 3 are located respectively at and . Find such that the center of mass of the system is located at the point .
and . Find such that the center of mass of the system is located at the point . فتح الحزمة
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80
Calculate the Maclaurin polynomial for .
for . فتح الحزمة
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