Question 1

Suppose (1, 1) is a critical point of a function f with continuous second derivatives.In the case of   hat can you say about f ? Select the correct Answer

Accepted Answer

A) f has a local maximum at (1,1) 
B) f has a saddle point at (1,1) 
C) f has a local minimum at (1,1) 
A) f has a local maximum at (1,1) 
B) f has a saddle point at (1,1) 
C) f has a local minimum at (1,1)

Question 2

Find the absolute extrema of the function   on the closed triangular region with vertices

Accepted Answer

Absolute m

Question 3

Find the limit   Hint: If   and   then   if and only if   Select the correct Answer

Accepted Answer

A) 1 
B) 0 
C)    
D)    
A) 1 
B) 0 
C)    
D)

Question 4

Select the correct Answer: for each question.
-At what point is the following function a local maximum?

Accepted Answer

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

Question 5

Select the correct Answer: for each question.
-Use the Chain Rule to find

Accepted Answer

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

Question 6

Find the domain and range of the function

Accepted Answer

The answer of Find the domain and range of the...

Question 7

Find the domain and range of the function

Accepted Answer

The answer of Find the domain and range of the...

Question 8

A boundary stripe 2 in.wide is painted around a rectangle whose dimensions are 100 ft by 240 ft.Use differentials to approximate the number of square feet of paint in the stripe.Select the correct Answer

Accepted Answer

A) 113   
B) 113.81   
C) 113.22   
D) 113.89   
E) 113.33   
A) 113   
B) 113.81   
C) 113.22   
D) 113.89   
E) 113.33

Question 9

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

Accepted Answer

A)    
B)    
C)    
D) 28 
E) none of these 
A)    
B)    
C)    
D) 28 
E) none of these

Question 10

Find the gradient of the function

Accepted Answer

The answer of Find the gradient of the function ...

Question 11

Select the correct Answer: for each question.
-Find the limit   Hint: If   if and only if

Accepted Answer

A)    
B) 0 
C)    
D) 1 
A)    
B) 0 
C)    
D) 1

Question 12

Evaluate the limit.

Accepted Answer

The answer of Evaluate the limit.  ...

Question 13

Find the differential of the function   Select the correct Answer

Accepted Answer

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

Question 14

Select the correct Answer: for each question.
-The ellipsoid   intersects the plane   in an ellipse.Find parametric equations for the tangent line to this ellipse at the point (1, 2, 2).

Accepted Answer

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

Question 15

Determine where the function   is continuous.

Accepted Answer

The answer of Determine where the function   is...

Question 16

Select the correct Answer: for each question.
-Find the directional derivative of   at the point (1, 3) in the direction toward the point (3, 1).Select the correct Answer

Accepted Answer

A)    
B)    
C)    
D) 28 
E) none of these 
A)    
B)    
C)    
D) 28 
E) none of these

Question 17

Find the points on the surface   that are closest to the origin.Select the correct Answer

Accepted Answer

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

Question 18

At what point is the following function a local minimum?   Select the correct Answer

Accepted Answer

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

Question 19

Find the first partial derivatives of the function.

Accepted Answer

The answer of Find the first partial derivatives of the...

Question 20

Select the correct Answer: for each question.
-The height of a hill (in feet) is given by   where x is the distance (in miles) east and y is the distance (in miles) north of your cabin.If you are at a point on the hill 1 mile north and 1 mile east of your cabin, what is the rate of change of the height of the hill (a) in a northerly direction and (b) in an easterly direction?

Accepted Answer

A) (a) 570 ft/mi, (b) 690 ft/mi 
B) (a) -570 ft/mi, (b) 690 ft/mi 
C) (a) 690 ft/mi, (b) 570 ft/mi 
D) (a) 690 ft/mi, (b) -570 ft/mi 
A) (a) 570 ft/mi, (b) 690 ft/mi 
B) (a) -570 ft/mi, (b) 690 ft/mi 
C) (a) 690 ft/mi, (b) 570 ft/mi 
D) (a) 690 ft/mi, (b) -570 ft/mi

Suppose (1, 1) is a critical point of a function f with continuous second derivatives.In the case of hat can you say about f ? Select the correct Answer

Find the absolute extrema of the function on the closed triangular region with vertices

Find the limit Hint: If and then if and only if Select the correct Answer

Select the correct Answer: for each question. -At what point is the following function a local maximum?

Select the correct Answer: for each question. -Use the Chain Rule to find

Find the domain and range of the function

Find the domain and range of the function

A boundary stripe 2 in.wide is painted around a rectangle whose dimensions are 100 ft by 240 ft.Use differentials to approximate the number of square feet of paint in the stripe.Select the correct Answer

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

Find the gradient of the function

Select the correct Answer: for each question. -Find the limit Hint: If if and only if

Evaluate the limit.

Find the differential of the function Select the correct Answer

Select the correct Answer: for each question. -The ellipsoid intersects the plane in an ellipse.Find parametric equations for the tangent line to this ellipse at the point (1, 2, 2).

Determine where the function is continuous.

Select the correct Answer: for each question. -Find the directional derivative of at the point (1, 3) in the direction toward the point (3, 1).Select the correct Answer

Find the points on the surface that are closest to the origin.Select the correct Answer

At what point is the following function a local minimum? Select the correct Answer

Find the first partial derivatives of the function.

Functions and Models

Limits and Derivatives

Differentiation Rules

Applications of Differentiation

Integrals

Applications of Integration

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

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

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Exam 14: Partial Derivatives

Suppose (1, 1) is a critical point of a function f with continuous second derivatives.In the case of hat can you say about f ? Select the correct Answer

Find the absolute extrema of the function on the closed triangular region with vertices

Find the limit Hint: If and then if and only if Select the correct Answer

Select the correct Answer: for each question. -At what point is the following function a local maximum?

Select the correct Answer: for each question. -Use the Chain Rule to find

Find the domain and range of the function

Find the domain and range of the function

A boundary stripe 2 in.wide is painted around a rectangle whose dimensions are 100 ft by 240 ft.Use differentials to approximate the number of square feet of paint in the stripe.Select the correct Answer

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

Find the gradient of the function

Select the correct Answer: for each question. -Find the limit Hint: If if and only if

Evaluate the limit.

Find the differential of the function Select the correct Answer

Select the correct Answer: for each question. -The ellipsoid intersects the plane in an ellipse.Find parametric equations for the tangent line to this ellipse at the point (1, 2, 2).

Determine where the function is continuous.

Select the correct Answer: for each question. -Find the directional derivative of at the point (1, 3) in the direction toward the point (3, 1).Select the correct Answer

Find the points on the surface that are closest to the origin.Select the correct Answer

At what point is the following function a local minimum? Select the correct Answer

Find the first partial derivatives of the function.

Functions and Models

Limits and Derivatives

Differentiation Rules

Applications of Differentiation

Integrals

Applications of Integration

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

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Filters