Question 1

Which of the following are Maclaurin polynomials of

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 2

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?

Accepted Answer

approximat

Question 3

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   .

Accepted Answer

The answer of Four particles with masses of 4, 5,...

Question 4

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   .)

Accepted Answer

The answer of A water tank is a rectangular tank...

Question 5

The quotient   is equal to:

Accepted Answer

A)    where   
B)    where   
C)    where   
D)    where   
E)  none of the above. 
A)    where   
B)    where   
C)    where   
D)    where   
E)  none of the above.

Question 6

Calculate the Maclaurin polynomial   for   .

Accepted Answer

The answer of Calculate the Maclaurin polynomial   for...

Question 7

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.

Accepted Answer

The answer of The plate shown in the figure, determined...

Question 8

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

Accepted Answer

The answer of Approximate the arc length of the curve...

Question 9

Find the centroid of the region enclosed by the graph of   , the tangent to the graph at   and the y-axis.

Accepted Answer

The answer of Find the centroid of the region enclosed...

Question 10

The Taylor polynomial   of   about   is:

Accepted Answer

A)    . 
B)    . 
C)    . 
D)    . 
E)    . 
A)    . 
B)    . 
C)    . 
D)    . 
E)    .

Question 11

Compute the arc length of   for   .

Accepted Answer

The answer of Compute the arc length of  ...

Question 12

The centroid of the region shown in the figure below enclosed by the graphs of   ,   , and   lies on:

Accepted Answer

A)  the line   
B)  the line   
C)  the line   
D)  the graph of   
E)  the graph of   
A)  the line   
B)  the line   
C)  the line   
D)  the graph of   
E)  the graph of

Question 13

Calculate the arc length of   over the interval

Accepted Answer

The answer of Calculate the arc length of  ...

Question 14

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

Accepted Answer

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. 
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.

Question 15

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   .

Accepted Answer

The answer of Find the centroid of the region in...

Question 16

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?

Accepted Answer

approximat

Question 17

Find the centroid of the region enclosed by the graphs   ,   ,   , and

Accepted Answer

The answer of Find the centroid of the region enclosed...

Question 18

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   .)

Accepted Answer

The answer of The plate shown in the figure is...

Question 19

Calculate the arc length of   over the interval   .

Accepted Answer

The answer of Calculate the arc length of  ...

Question 20

Calculate the arc length of   over the interval [1, 5].

Accepted Answer

The answer of Calculate the arc length of  ...

Which of the following are Maclaurin polynomials of

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?

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 .

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 .)

The quotient is equal to:

Calculate the Maclaurin polynomial for .

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.

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

Find the centroid of the region enclosed by the graph of , the tangent to the graph at and the y-axis.

The Taylor polynomial of about is:

Compute the arc length of for .

The centroid of the region shown in the figure below enclosed by the graphs of , , and lies on:

Calculate the arc length of over the interval

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

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 .

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?

Find the centroid of the region enclosed by the graphs , , , and

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 .)

Calculate the arc length of over the interval .

Calculate the arc length of over the interval [1, 5].

Precalculus Review

Limits

Differentiation

Applications of the Derivative

The Integral

Applications of the Integral

Exponential Functions

Techniques of Integration

Introduction to Differential Equations

Infinite Series

Parametric Equations, Polar Coordinates, and Conic Sections

Vector Geometry

Calculus of Vector-Valued Functions

Differentiation in Several Variables

Multiple Integration

Line and Surface Integrals

Fundamental Theorems of Vector Analysis

Filters

Exam 9: Further Applications of the Integral and Taylor Polynomials

Which of the following are Maclaurin polynomials of

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?

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 .

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 .)

The quotient is equal to:

Calculate the Maclaurin polynomial for .

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.

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

Find the centroid of the region enclosed by the graph of , the tangent to the graph at and the y-axis.

The Taylor polynomial of about is:

Compute the arc length of for .

The centroid of the region shown in the figure below enclosed by the graphs of , , and lies on:

Calculate the arc length of over the interval

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

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 .

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?

Find the centroid of the region enclosed by the graphs , , , and

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 .)

Calculate the arc length of over the interval .

Calculate the arc length of over the interval [1, 5].

Precalculus Review

Limits

Differentiation

Applications of the Derivative

The Integral

Applications of the Integral

Exponential Functions

Techniques of Integration

Introduction to Differential Equations

Infinite Series

Parametric Equations, Polar Coordinates, and Conic Sections

Vector Geometry

Calculus of Vector-Valued Functions

Differentiation in Several Variables

Multiple Integration

Line and Surface Integrals

Fundamental Theorems of Vector Analysis

Filters