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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
Exam 10: Introduction to Differential Equations73 Questionsadd course
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Exam 12: Parametric Equations, Polar Coordinates, and Conic Sections71 Questionsadd course
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An infinite plate shown in the figure below, bounded by the graphs of 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 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 the y-axis, is submerged vertically in water, with its top 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 ) ft below the water surface. Calculate the fluid force on a side of the plate. (The density of water is 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 ) ) 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 )

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Question 21

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

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Question 22

A plate bounded by the functions 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 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? on the interval 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? 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?

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Question 23

Calculate the arc length of the curve Calculate the arc length of the curve over the interval . over the interval Calculate the arc length of the curve over the interval . .

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Question 24

Calculate the Maclaurin polynomial Calculate the Maclaurin polynomial for . for Calculate the Maclaurin polynomial for . .

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Question 25

An infinite plate shown in the figure below, bounded by the graphs of 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 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 the y-axis, is submerged vertically in water, with its top 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 ) ft below the water surface. Calculate the fluid force on a side of the plate. (The density of water is 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 ) ) 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 )

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Question 26

Evaluate Evaluate using Taylor polynomials. using Taylor polynomials.

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Question 27

Let Let . A) Write the Maclaurin polynomial for . B) Use Taylor's Theorem for to write an integration formula. . A) Write the Maclaurin polynomial Let . A) Write the Maclaurin polynomial for . B) Use Taylor's Theorem for to write an integration formula. for Let . A) Write the Maclaurin polynomial for . B) Use Taylor's Theorem for to write an integration formula. . B) Use Taylor's Theorem for Let . A) Write the Maclaurin polynomial for . B) Use Taylor's Theorem for to write an integration formula. to write an integration formula.

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Question 28

Calculate the arc length of the curve Calculate the arc length of the curve over the interval . over the interval Calculate the arc length of the curve over the interval . .

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Question 29

Evaluate Evaluate . .

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Question 30

Compute the arc length of Compute the arc length of over the interval [0, 2]. over the interval [0, 2].

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Question 31

Find the centroid of the quarter ring shown in the figure below. Find the centroid of the quarter ring shown in the figure below.

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Question 32

Find the centroid of the region enclosed by the curves Find the centroid of the region enclosed by the curves and . and Find the centroid of the region enclosed by the curves and . . Find the centroid of the region enclosed by the curves and .

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Question 33

Which of the following is a Maclaurin polynomial of Which of the following is a Maclaurin polynomial of ? ?

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Question 34

Find Find for the lamina of uniform density occupying the region under from . for the lamina of uniform density Find for the lamina of uniform density occupying the region under from . occupying the region under Find for the lamina of uniform density occupying the region under from . from Find for the lamina of uniform density occupying the region under from . .

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Question 35

Calculate the arc length of Calculate the arc length of over the interval . over the interval Calculate the arc length of over the interval . .

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Question 36

Let Let denote the remainder , where is the Maclaurin polynomial for If , find . denote the Let denote the remainder , where is the Maclaurin polynomial for If , find . remainder Let denote the remainder , where is the Maclaurin polynomial for If , find . , where Let denote the remainder , where is the Maclaurin polynomial for If , find . is the Let denote the remainder , where is the Maclaurin polynomial for If , find . Maclaurin polynomial for Let denote the remainder , where is the Maclaurin polynomial for If , find . If Let denote the remainder , where is the Maclaurin polynomial for If , find . , find Let denote the remainder , where is the Maclaurin polynomial for If , find . .

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Question 37

Compute Compute for centered at . Use the error bound to find the maximum possible size of error of . for Compute for centered at . Use the error bound to find the maximum possible size of error of . centered at Compute for centered at . Use the error bound to find the maximum possible size of error of . . Use the error bound to find the maximum possible size of error of Compute for centered at . Use the error bound to find the maximum possible size of error of . .

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Question 38

Find the centroid of the portion of the unit circle lying within the first three quadrants.

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Question 39

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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