Question 1

Find all the second partial derivatives of

Accepted Answer

The answer of Find all the second partial derivatives of...

Question 2

Use Lagrange multipliers to find the maximum and the minimum of f subject to the given constraint(s).

Accepted Answer

maximum =

Question 3

Find the local and absolute extreme values of the function on the given interval.   ,

Accepted Answer

The answer of Find the local and absolute extreme values...

Question 4

The graphs of   and   are given.
Find the values of   and   .

Accepted Answer

The answer of The graphs of   and ...

Question 5

Determine whether the series is convergent or divergent by expressing   as a telescoping sum. If it is convergent, find its sum.   .

Accepted Answer

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

Question 6

If an equation of the tangent line to the curve   at the point where

Accepted Answer

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

Question 7

Find   for the function   .

Accepted Answer

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

Question 8

Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.

Accepted Answer

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

Question 9

The top of a ladder slides down a vertical wall at a rate of 0.1m/s . At the moment when the bottom of the ladder is 3 m from the wall, it slides away from the wall at a rate of 0.2 m/s . How long is the ladder?

Accepted Answer

The answer of The top of a ladder slides down...

Question 10

The graphs of   and   are given. For what values of x is   ?

Accepted Answer

A) -4, 12 
B) 4, 2 
C)    
D) 0 
E)    
A) -4, 12 
B) 4, 2 
C)    
D) 0 
E)

Question 11

How would you define   in order to make f continuous at   ?

Accepted Answer

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

Question 12

Calculate the given quantities if

Accepted Answer

The answer of Calculate the given quantities if  ...

Question 13

Solve the initial-value problem.

Accepted Answer

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

Question 14

If   , evaluate   .

Accepted Answer

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

Question 15

Find the unit tangent vector for the curve given by   .

Accepted Answer

The answer of Find the unit tangent vector for the...

Question 16

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

Accepted Answer

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

Question 17

Use Euler's method with step size 0.1 to estimate   , where   is the solution of the initial-value problem. Round your answer to four decimal places.

Accepted Answer

The answer of Use Euler's method with step size 0.1...

Question 18

If   , evaluate the difference quotient   .

Accepted Answer

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

Question 19

Find the sum of the series.

Accepted Answer

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

Question 20

Evaluate the integral.

Accepted Answer

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

Find all the second partial derivatives of

Use Lagrange multipliers to find the maximum and the minimum of f subject to the given constraint(s).

Find the local and absolute extreme values of the function on the given interval. ,

The graphs of and are given. Find the values of and .

Determine whether the series is convergent or divergent by expressing as a telescoping sum. If it is convergent, find its sum. .

If an equation of the tangent line to the curve at the point where

Find for the function .

Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.

The top of a ladder slides down a vertical wall at a rate of 0.1m/s . At the moment when the bottom of the ladder is 3 m from the wall, it slides away from the wall at a rate of 0.2 m/s . How long is the ladder?

The graphs of and are given. For what values of x is ?

How would you define in order to make f continuous at ?

Calculate the given quantities if

Solve the initial-value problem.

If , evaluate .

Find the unit tangent vector for the curve given by .

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

Use Euler's method with step size 0.1 to estimate , where is the solution of the initial-value problem. Round your answer to four decimal places.

If , evaluate the difference quotient .

Find the sum of the series.

Evaluate the 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

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Exam 18: Final Exam

Find all the second partial derivatives of

Use Lagrange multipliers to find the maximum and the minimum of f subject to the given constraint(s).

Find the local and absolute extreme values of the function on the given interval. ,

The graphs of and are given. Find the values of and .

Determine whether the series is convergent or divergent by expressing as a telescoping sum. If it is convergent, find its sum. .

If an equation of the tangent line to the curve at the point where

Find for the function .

Set up an integral that represents the length of the curve. Then use your calculator to find the length correct to four decimal places.

The top of a ladder slides down a vertical wall at a rate of 0.1m/s . At the moment when the bottom of the ladder is 3 m from the wall, it slides away from the wall at a rate of 0.2 m/s . How long is the ladder?

The graphs of and are given. For what values of x is ?

How would you define in order to make f continuous at ?

Calculate the given quantities if

Solve the initial-value problem.

If , evaluate .

Find the unit tangent vector for the curve given by .

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

Use Euler's method with step size 0.1 to estimate , where is the solution of the initial-value problem. Round your answer to four decimal places.

If , evaluate the difference quotient .

Find the sum of the series.

Evaluate the 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