Question 1

Find the domain and range and describe the level curves for the function f(x,y).
-f(x, y) =

Accepted Answer

A)   Domain: all points in the first quadrant of the xy-plane; range: all real numbers; level curves: lines x + y = c 
B)   Domain: all points in the first quadrant of the xy-plane; range: real numbers z > 0; level curves: lines x + y = c 
C)   Domain: all points in the xy-plane; range: real numbers z > 0; level curves: lines x + y = c 
D)   Domain: all points in the xy-plane; range: all real numbers; level curves: lines x + y = c 
A)   Domain: all points in the first quadrant of the xy-plane; range: all real numbers; level curves: lines x + y = c 
B)   Domain: all points in the first quadrant of the xy-plane; range: real numbers z > 0; level curves: lines x + y = c 
C)   Domain: all points in the xy-plane; range: real numbers z > 0; level curves: lines x + y = c 
D)   Domain: all points in the xy-plane; range: all real numbers; level curves: lines x + y = c

Question 2

Solve the problem.
-

Accepted Answer

A)  -0.03 watts 
B)  0.13 watts 
C)  -0.13 watts 
D)  0.03 watts 
A)  -0.03 watts 
B)  0.13 watts 
C)  -0.13 watts 
D)  0.03 watts

Question 3

Match the surface show below to the graph of its level curves.
-

Accepted Answer

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

Question 4

Find the limit.
-    x -   y + z

Accepted Answer

A)  8 
B)  9 
C)  6 
D)  7 
A)  8 
B)  9 
C)  6 
D)  7

Question 5

Find all the first order partial derivatives for the following function.  
-f(x ,y, z) = (sin xy)(cos y   )

Accepted Answer

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

Question 6

Solve the problem.
-Find the point on the sphere   that is closest to the point

Accepted Answer

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

Question 7

Match the surface show below to the graph of its level curves.
-

Accepted Answer

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

Question 8

Find all the first order partial derivatives for the following function.  
-f(x, y, z) = cos x   yz

Accepted Answer

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

Question 9

Sketch the surface z = f(x,y).
-f(x, y) = 4   + 4   + 2

Accepted Answer

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

Find the domain and range and describe the level curves for the function f(x,y). -f(x, y) =

Solve the problem. -

Match the surface show below to the graph of its level curves. -

Find the limit. - x - y + z

Find all the first order partial derivatives for the following function. -f(x ,y, z) = (sin xy)(cos y )

Solve the problem. -Find the point on the sphere that is closest to the point

Match the surface show below to the graph of its level curves. -

Find all the first order partial derivatives for the following function. -f(x, y, z) = cos x yz

Sketch the surface z = f(x,y). -f(x, y) = 4 + 4 + 2

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Multiple Integration

Vector Calculus

Filters

Exam 15: Functions of Several Variables

Find the domain and range and describe the level curves for the function f(x,y). -f(x, y) =

Solve the problem. -

Match the surface show below to the graph of its level curves. -

Find the limit. - x - y + z

Find all the first order partial derivatives for the following function. -f(x ,y, z) = (sin xy)(cos y )

Solve the problem. -Find the point on the sphere that is closest to the point

Match the surface show below to the graph of its level curves. -

Find all the first order partial derivatives for the following function. -f(x, y, z) = cos x yz

Sketch the surface z = f(x,y). -f(x, y) = 4 + 4 + 2

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Multiple Integration

Vector Calculus

Filters