Question 1

Use polar coordinates to find the limit   [Hint: Let   and note that

Accepted Answer

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

Question 2

Find the limit   for the function

Accepted Answer

A) -5y 
B)    
C)    
D) 5y 
E) 8x 
A) -5y 
B)    
C)    
D) 5y 
E) 8x E

Question 3

Sketch the surface given by the function.

Accepted Answer

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

Question 4

Find the limit.

Accepted Answer

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

Question 5

Find the limit   for the function

Accepted Answer

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

Question 6

The average length of time that a customer waits in line for service is   where y is the average arrival rate, written as the number of customers per unit of time, and x is the average service rate, written in the same units.Evaluate   Note: x
And y are given as the number of customers per hour.

Accepted Answer

A) 7 min 
B) 5 min 
C) 3 min 
D) 4 min 
E) 6 min 
A) 7 min 
B) 5 min 
C) 3 min 
D) 4 min 
E) 6 min

Question 7

Find the limit.

Accepted Answer

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

Question 8

Use spherical coordinates to find the limit   [Hint: Let   nd note that   implies

Accepted Answer

A) 6 
B) 9 
C) 1 
D) 7 
E)    
A) 6 
B) 9 
C) 1 
D) 7 
E)

Question 9

Sketch the level curves for the function   for the given c-values

Accepted Answer

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

Question 10

Find and simplify the function   at the given value

Accepted Answer

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

Question 11

Sketch the level curves of the function   for the given c-values

Accepted Answer

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

Question 12

Use polar coordinates and L'Hopital's Rule to find the limit.

Accepted Answer

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

Question 13

Determine the continuity of the function

Accepted Answer

A) continuous except at   
B) continuous except at   
C) continuous except at   
D) continuous except at   
E) continuous everywhere 
A) continuous except at   
B) continuous except at   
C) continuous except at   
D) continuous except at   
E) continuous everywhere

Question 14

Describe the level curves of the function.Sketch the level curves for the given c- values.

Accepted Answer

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

Question 15

Determine the continuity of the function

Accepted Answer

A) continuous except at   
B) continuous except at   
C) continuous for all   
D) continuous for all   
E) continuous everywhere 
A) continuous except at   
B) continuous except at   
C) continuous for all   
D) continuous for all   
E) continuous everywhere

Question 16

Find and simplify the function   at the given value

Accepted Answer

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

Question 17

Find the limit.

Accepted Answer

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

Question 18

Find and simplify the function   at the given value

Accepted Answer

A) -42 
B) -14 
C) 42 
D) 14 
E)    
A) -42 
B) -14 
C) 42 
D) 14 
E)

Question 19

Determine the continuity of the composite function   and

Accepted Answer

A) continuous except at   
B) continuous for all   
C) continuous for all   
D) continuous except at   
E) continuous everywhere 
A) continuous except at   
B) continuous for all   
C) continuous for all   
D) continuous except at   
E) continuous everywhere

Question 20

Determine the continuity of the function

Accepted Answer

A) continuous except at   
B) continuous except at   
C) continuous except at   
D) continuous except at   
E) continuous everywhere 
A) continuous except at   
B) continuous except at   
C) continuous except at   
D) continuous except at   
E) continuous everywhere

Use polar coordinates to find the limit [Hint: Let and note that

Find the limit for the function

Sketch the surface given by the function.

Find the limit.

Find the limit for the function

The average length of time that a customer waits in line for service is where y is the average arrival rate, written as the number of customers per unit of time, and x is the average service rate, written in the same units.Evaluate Note: x And y are given as the number of customers per hour.

Find the limit.

Use spherical coordinates to find the limit [Hint: Let nd note that implies

Sketch the level curves for the function for the given c-values

Find and simplify the function at the given value

Sketch the level curves of the function for the given c-values

Use polar coordinates and L'Hopital's Rule to find the limit.

Determine the continuity of the function

Describe the level curves of the function.Sketch the level curves for the given c- values.

Determine the continuity of the function

Find and simplify the function at the given value

Find the limit.

Find and simplify the function at the given value

Determine the continuity of the composite function and

Determine the continuity of the function

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Logarithmic, Exponential, and Other Transcendental Functions

Differential Equations

Applications of Integration

Integration Techniques, Lhôpitals Rule, and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Multiple Integration

Vector Analysis

Additional Topics in Differential Equations

Preparation for Calculus

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Exam 13: Functions of Several Variables

Use polar coordinates to find the limit [Hint: Let and note that

Find the limit for the function

Sketch the surface given by the function.

Find the limit.

Find the limit for the function

The average length of time that a customer waits in line for service is where y is the average arrival rate, written as the number of customers per unit of time, and x is the average service rate, written in the same units.Evaluate Note: x And y are given as the number of customers per hour.

Find the limit.

Use spherical coordinates to find the limit [Hint: Let nd note that implies

Sketch the level curves for the function for the given c-values

Find and simplify the function at the given value

Sketch the level curves of the function for the given c-values

Use polar coordinates and L'Hopital's Rule to find the limit.

Determine the continuity of the function

Describe the level curves of the function.Sketch the level curves for the given c- values.

Determine the continuity of the function

Find and simplify the function at the given value

Find the limit.

Find and simplify the function at the given value

Determine the continuity of the composite function and

Determine the continuity of the function

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Logarithmic, Exponential, and Other Transcendental Functions

Differential Equations

Applications of Integration

Integration Techniques, Lhôpitals Rule, and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Multiple Integration

Vector Analysis

Additional Topics in Differential Equations

Preparation for Calculus

Filters