Question 1

How many nth-order partial derivatives does a function of two variables have?

Accepted Answer

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

Question 2

Use the Chain Rule to find

Accepted Answer

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

Question 3

Find the limit.

Accepted Answer

The answer of Find the limit.  ...

Question 4

Find   for the function

Accepted Answer

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

Question 5

Find the differential of the function

Accepted Answer

The answer of Find the differential of the function ...

Question 6

Find the limit

Accepted Answer

A)  34 
B)  16 
C)  80 
D)  260 
A)  34 
B)  16 
C)  80 
D)  260

Question 7

Find the indicated partial derivative.

Accepted Answer

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

Question 8

Use Lagrange multipliers to find the maximum value of the function subject to the given constraint.

Accepted Answer

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

Question 9

Find the equation of the normal line to the given surface at the specified point.

Accepted Answer

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

Question 10

Find the directional derivative of the function   at the point   in the direction of the unit vector that makes the angle   with the positive x-axis.

Accepted Answer

A)  1 
B)    
C)  11 
D)    
A)  1 
B)    
C)  11 
D)

Question 11

Find the limit

Accepted Answer

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

Question 12

Find the equation of the tangent plane to the given surface at the specified point.

Accepted Answer

The answer of Find the equation of the tangent plane...

Question 13

Find the first partial derivatives of the function.

Accepted Answer

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

Question 14

Determine where the function   is continuous.

Accepted Answer

The answer of Determine where the function   is...

Question 15

Find the dimensions of the rectangular box with largest volume if the total surface area is given as     .

Accepted Answer

A)    cm,1.75 cm,1.75 cm 
B)    cm,   cm,   cm 
C)    cm,   cm,   cm 
D)    cm,   cm,3.5 cm 
E)    cm,   cm,1.75 cm 
A)    cm,1.75 cm,1.75 cm 
B)    cm,   cm,   cm 
C)    cm,   cm,   cm 
D)    cm,   cm,3.5 cm 
E)    cm,   cm,1.75 cm

Question 16

Find   for   .

Accepted Answer

The answer of Find   for   ....

Question 17

Find the limit

Accepted Answer

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

Question 18

Find the differential of the function

Accepted Answer

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

Question 19

A contour map for a function f is shown.Use it to estimate the value of   .

Accepted Answer

A)  78 
B)  35 
C)  48 
D)  28 
E)  71 
A)  78 
B)  35 
C)  48 
D)  28 
E)  71

Question 20

Let   and suppose that   changes from   to   
(a)Compute   
(b)Compute

Accepted Answer

The answer of Let   and suppose that ...

How many nth-order partial derivatives does a function of two variables have?

Use the Chain Rule to find

Find the limit.

Find for the function

Find the differential of the function

Find the limit

Find the indicated partial derivative.

Use Lagrange multipliers to find the maximum value of the function subject to the given constraint.

Find the equation of the normal line to the given surface at the specified point.

Find the directional derivative of the function at the point in the direction of the unit vector that makes the angle with the positive x-axis.

Find the limit

Find the equation of the tangent plane to the given surface at the specified point.

Find the first partial derivatives of the function.

Determine where the function is continuous.

Find the dimensions of the rectangular box with largest volume if the total surface area is given as .

Find for .

Find the limit

Find the differential of the function

A contour map for a function f is shown.Use it to estimate the value of .

Let and suppose that changes from to (a)Compute (b)Compute

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Integrals

Techniques of Integration

Applications of Integration

Series

Parametric Equations and Polar Coordinates

Ectors and the Geometry of Space

Multiple Integrals

Vector Calculus

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Exam 11: Partial Derivatives

How many nth-order partial derivatives does a function of two variables have?

Use the Chain Rule to find

Find the limit.

Find for the function

Find the differential of the function

Find the limit

Find the indicated partial derivative.

Use Lagrange multipliers to find the maximum value of the function subject to the given constraint.

Find the equation of the normal line to the given surface at the specified point.

Find the directional derivative of the function at the point in the direction of the unit vector that makes the angle with the positive x-axis.

Find the limit

Find the equation of the tangent plane to the given surface at the specified point.

Find the first partial derivatives of the function.

Determine where the function is continuous.

Find the dimensions of the rectangular box with largest volume if the total surface area is given as .

Find for .

Find the limit

Find the differential of the function

A contour map for a function f is shown.Use it to estimate the value of .

Let and suppose that changes from to (a)Compute (b)Compute

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Applications of Differentiation

Integrals

Techniques of Integration

Applications of Integration

Series

Parametric Equations and Polar Coordinates

Ectors and the Geometry of Space

Multiple Integrals

Vector Calculus

Filters