Question 1

Find the directional derivative of   at the point (1, 3) in the direction toward the point (3, 1).

Accepted Answer

A)    
B)    
C)    
D)    
E) None of these 
A)    
B)    
C)    
D)    
E) None of these B

Question 2

Find a nonzero vector orthogonal to the plane through the points P, Q, and R.

Accepted Answer

A)    
B)    
C)    
D)    
E) None of these 
A)    
B)    
C)    
D)    
E) None of these C

Question 3

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

Accepted Answer

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

Question 4

Find the average value of the function   on the interval   . Round your answer to 3 decimal places.

Accepted Answer

A) 0.3 
B)    
C) 0.288 
D) 6.228 
E) 12 
A) 0.3 
B)    
C) 0.288 
D) 6.228 
E) 12

Question 5

Find the length of the curve.

Accepted Answer

A)    
B) 25.05   
C) 13.05 
D) 36.05 
E) None of these 
A)    
B) 25.05   
C) 13.05 
D) 36.05 
E) None of these

Question 6

Find the area of the region that lies under the given curve. Round the answer to three decimal places.

Accepted Answer

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

Question 7

Evaluate the integral using the indicated trigonometric substitution.

Accepted Answer

The answer of Evaluate the integral using the indicated trigonometric...

Question 8

A piece of wire   m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut for the square so that the total area enclosed is a minimum? Round your answer to the nearest hundredth.

Accepted Answer

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

Question 9

Use spherical coordinates. Evaluate   , where   is the ball with center the origin and radius   .

Accepted Answer

A)    
B)    
C)    
D)    
E) None of these 
A)    
B)    
C)    
D)    
E) None of these

Question 10

Find the volume of the resulting solid if the region under the curve   from   to   is rotated about the x-axis. Round your answer to four decimal places.

Accepted Answer

The answer of Find the volume of the resulting solid...

Question 11

Find the volume of the given solid.
Under the paraboloid   and above the rectangle   .

Accepted Answer

The answer of Find the volume of the given solid.
Under...

Question 12

If   , find the Riemann sum with n = 5 correct to 3 decimal places, taking the sample points to be midpoints.

Accepted Answer

The answer of If   , find the Riemann...

Question 13

Find the area of the region that is bounded by the given curve and lies in the specified sector.

Accepted Answer

The answer of Find the area of the region that...

Question 14

The acceleration function (in m / s2) and the initial velocity are given for a particle moving along a line. Find the velocity at time t and the distance traveled during the given time interval.

Accepted Answer

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

Question 15

The masses   are located at the point   . Find the moments   and   and the center of mass of the system.   ;

Accepted Answer

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

Question 16

Which equation does the function   satisfy?

Accepted Answer

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

Question 17

Solve the initial-value problem.

Accepted Answer

The answer of Solve the initial-value problem.  ...

Question 18

Find the volume of the given solid.
Under the paraboloid   and above the rectangle   .

Accepted Answer

The answer of Find the volume of the given solid.
Under...

Question 19

Evaluate the integral.

Accepted Answer

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

Question 20

Evaluate the line integral.

Accepted Answer

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

Find the directional derivative of at the point (1, 3) in the direction toward the point (3, 1).

Find a nonzero vector orthogonal to the plane through the points P, Q, and R.

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

Find the average value of the function on the interval . Round your answer to 3 decimal places.

Find the length of the curve.

Find the area of the region that lies under the given curve. Round the answer to three decimal places.

Evaluate the integral using the indicated trigonometric substitution.

A piece of wire m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut for the square so that the total area enclosed is a minimum? Round your answer to the nearest hundredth.

Use spherical coordinates. Evaluate , where is the ball with center the origin and radius .

Find the volume of the resulting solid if the region under the curve from to is rotated about the x-axis. Round your answer to four decimal places.

Find the volume of the given solid. Under the paraboloid and above the rectangle .

If , find the Riemann sum with n = 5 correct to 3 decimal places, taking the sample points to be midpoints.

Find the area of the region that is bounded by the given curve and lies in the specified sector.

The acceleration function (in m / s²) and the initial velocity are given for a particle moving along a line. Find the velocity at time t and the distance traveled during the given time interval.

The masses are located at the point . Find the moments and and the center of mass of the system. ;

Which equation does the function satisfy?

Solve the initial-value problem.

Find the volume of the given solid. Under the paraboloid and above the rectangle .

Evaluate the integral.

Evaluate the line integral.

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Filters

Exam 18: Final Exam

Find the directional derivative of at the point (1, 3) in the direction toward the point (3, 1).

Find a nonzero vector orthogonal to the plane through the points P, Q, and R.

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

Find the average value of the function on the interval . Round your answer to 3 decimal places.

Find the length of the curve.

Find the area of the region that lies under the given curve. Round the answer to three decimal places.

Evaluate the integral using the indicated trigonometric substitution.

A piece of wire m long is cut into two pieces. One piece is bent into a square and the other is bent into an equilateral triangle. How should the wire be cut for the square so that the total area enclosed is a minimum? Round your answer to the nearest hundredth.

Use spherical coordinates. Evaluate , where is the ball with center the origin and radius .

Find the volume of the resulting solid if the region under the curve from to is rotated about the x-axis. Round your answer to four decimal places.

Find the volume of the given solid. Under the paraboloid and above the rectangle .

If , find the Riemann sum with n = 5 correct to 3 decimal places, taking the sample points to be midpoints.

Find the area of the region that is bounded by the given curve and lies in the specified sector.

The acceleration function (in m / s2) and the initial velocity are given for a particle moving along a line. Find the velocity at time t and the distance traveled during the given time interval.

The masses are located at the point . Find the moments and and the center of mass of the system. ;

Which equation does the function satisfy?

Solve the initial-value problem.

Find the volume of the given solid. Under the paraboloid and above the rectangle .

Evaluate the integral.

Evaluate the line integral.

Functions and Limits

Derivatives

Applications of Differentiation

Integrals

Applications of Integration

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Filters

The acceleration function (in m / s²) and the initial velocity are given for a particle moving along a line. Find the velocity at time t and the distance traveled during the given time interval.