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Exam 9: Further Applications of the Integral and Taylor Polynomials

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Exam 1: Precalculus Review74 Questionsadd course
Exam 2: Limits97 Questionsadd course
Exam 3: Differentiation81 Questionsadd course
Exam 4: Applications of the Derivative77 Questionsadd course
Exam 5: The Integral82 Questionsadd course
Exam 6: Applications of the Integral80 Questionsadd course
Exam 7: Exponential Functions106 Questionsadd course
Exam 8: Techniques of Integration101 Questionsadd course
Exam 9: Further Applications of the Integral and Taylor Polynomials100 Questionsadd course
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Exam 11: Infinite Series95 Questionsadd course
Exam 12: Parametric Equations, Polar Coordinates, and Conic Sections71 Questionsadd course
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Exam 14: Calculus of Vector-Valued Functions99 Questionsadd course
Exam 15: Differentiation in Several Variables95 Questionsadd course
Exam 16: Multiple Integration98 Questionsadd course
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Let 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 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 = ) , the positive x-axis, and the negative y-axis. Calculate the fluid force on a side of the plate in the shape 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 = ) if the water surface is at 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 = ) . (The density of water is w = 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 = ) ) 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 = )

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Question 81

Compute the surface area of revolution of Compute the surface area of revolution of about the x-axis over the interval . about the x-axis over the interval Compute the surface area of revolution of about the x-axis over the interval . .

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Question 82

The third Taylor polynomial of The third Taylor polynomial of about is: about The third Taylor polynomial of about is: is:

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Question 83

A thin plate shown in the figure, bounded by the graphs 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 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 the x-axis, is submerged vertically in a fluid of density 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. so that its top is level with the fluid surface. Calculate the fluid pressure on a side of the plate if 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. is given in terms of weight per unit volume. 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.

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Question 84

Find the centroid of the shaded region in the figure below. Find the centroid of the shaded region in the figure below.

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Question 85

Approximate the arc length of the curve Approximate the arc length of the curve over the interval using Simpson's Rule . over the interval Approximate the arc length of the curve over the interval using Simpson's Rule . using Simpson's Rule Approximate the arc length of the curve over the interval using Simpson's Rule . .

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Question 86

Let Let . What is the coefficient of in the ninth Maclaurin polynomial of ? . What is the coefficient of Let . What is the coefficient of in the ninth Maclaurin polynomial of ? in the ninth Maclaurin polynomial of Let . What is the coefficient of in the ninth Maclaurin polynomial of ? ?

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Question 87

Let Let denote the remainder , where is the Maclaurin polynomial for If , then is: denote the Let denote the remainder , where is the Maclaurin polynomial for If , then is: remainder Let denote the remainder , where is the Maclaurin polynomial for If , then is: , where Let denote the remainder , where is the Maclaurin polynomial for If , then is: is the Let denote the remainder , where is the Maclaurin polynomial for If , then is: Maclaurin polynomial for Let denote the remainder , where is the Maclaurin polynomial for If , then is: If Let denote the remainder , where is the Maclaurin polynomial for If , then is: , then Let denote the remainder , where is the Maclaurin polynomial for If , then is: is:

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Question 88

Let Let be the solid obtained by revolving the infinite graph of about the x-axis for . Which of the following statements is correct? be the solid obtained by revolving the infinite graph of Let be the solid obtained by revolving the infinite graph of about the x-axis for . Which of the following statements is correct? about the x-axis for Let be the solid obtained by revolving the infinite graph of about the x-axis for . Which of the following statements is correct? . Let be the solid obtained by revolving the infinite graph of about the x-axis for . Which of the following statements is correct? Which of the following statements is correct?

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Question 89

Find the center of mass of the region enclosed by the graphs of Find the center of mass of the region enclosed by the graphs of and . and Find the center of mass of the region enclosed by the graphs of and . . Find the center of mass of the region enclosed by the graphs of and .

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Question 90

Find the center of mass of the region enclosed by the graphs of Find the center of mass of the region enclosed by the graphs of and . and Find the center of mass of the region enclosed by the graphs of and . . Find the center of mass of the region enclosed by the graphs of and .

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Question 91

The quotient The quotient is equal to: is equal to:

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Question 92

Let Let be the Taylor polynomial of centered at . Which of the following statements is correct? be the Taylor polynomial of Let be the Taylor polynomial of centered at . Which of the following statements is correct? centered at Let be the Taylor polynomial of centered at . Which of the following statements is correct? . Which of the following statements is correct?

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Question 93

Find the centroid of the region lying between the graphs of Find the centroid of the region lying between the graphs of and over the interval . and Find the centroid of the region lying between the graphs of and over the interval . over the interval Find the centroid of the region lying between the graphs of and over the interval . . Find the centroid of the region lying between the graphs of and over the interval . Find the centroid of the region lying between the graphs of and over the interval .

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Question 94

The plate determined by the region between the graphs of 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 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. is submerged in a fluid with density 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. , with its top touching the surface of the fluid. Find the fluid pressure on a side of the plate if 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. is given in terms of weight per unit volume. 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.

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Question 95

If If is the Maclaurin polynomial of , then is: is the Maclaurin polynomial of If is the Maclaurin polynomial of , then is: , then If is the Maclaurin polynomial of , then is: is:

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Question 96

Let 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 be an invertible function such that 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 and 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 . Let 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 be the region enclosed by the graphs of 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 and 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 over the interval 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 . The centroid of 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 lies on

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Question 97

The centroid of the region enclosed by the graphs of The centroid of the region enclosed by the graphs of and lies on the line and The centroid of the region enclosed by the graphs of and lies on the line lies on the line

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Question 98

Find the centroid of the shaded region in the figure below. Find the centroid of the shaded region in the figure below.

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Question 99

Calculate the Taylor polynomial Calculate the Taylor polynomial for about . for Calculate the Taylor polynomial for about . about Calculate the Taylor polynomial for about . .

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Question 100
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