Question 1

Solve the problem.
-Find the equation for the tangent plane to the surface   at the point

Accepted Answer

A)  x + y + z = 0 
B)  x - y = 0 
C)  z = 0 
D)  x + y = 0 
A)  x + y + z = 0 
B)  x - y = 0 
C)  z = 0 
D)  x + y = 0

Question 2

Solve the problem.
-Evaluate   at t = 9 for the function w(x, y, z) =   ; x = t, y = t, z =   .

Accepted Answer

A)  - 16/9 e 
B)  16/9 e 
C)  0 
D)  16/9 
A)  - 16/9 e 
B)  16/9 e 
C)  0 
D)  16/9

Question 3

Solve the problem.
-Evaluate   at (u, v) = ( 5, 3) for the function w(x, y, z) = xz + yz -   ; x = uv, y = uv, z = u.

Accepted Answer

A)  0 
B)  60 
C)  50 
D)  -10 
A)  0 
B)  60 
C)  50 
D)  -10

Question 4

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 xy-plane; range: all real numbers; level curves: parabolas  y= cxS1U1P12 S1S1P0- 6 
B)   Domain: all points in the xy-plane; range: real numbers z ≥ 0; level curves: parabolas   y= cxS1U1P12 S1S1P0- 6 
C)   Domain: all points in the xy-plane excluding x = 0; range: all real numbers; level curves: parabolas   y= cxS1U1P12 S1S1P0- 6 
D)   Domain: all points in the xy-plane excluding x = 0; range: real numbers z ≥ 0; level curves: parabolas    y= cxS1U1P12 S1S1P0- 6 
A)   Domain: all points in the xy-plane; range: all real numbers; level curves: parabolas  y= cxS1U1P12 S1S1P0- 6 
B)   Domain: all points in the xy-plane; range: real numbers z ≥ 0; level curves: parabolas   y= cxS1U1P12 S1S1P0- 6 
C)   Domain: all points in the xy-plane excluding x = 0; range: all real numbers; level curves: parabolas   y= cxS1U1P12 S1S1P0- 6 
D)   Domain: all points in the xy-plane excluding x = 0; range: real numbers z ≥ 0; level curves: parabolas    y= cxS1U1P12 S1S1P0- 6

Question 5

Solve the problem.
-Find the distance from the point   to the plane

Accepted Answer

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

Question 6

Solve the problem.
-Evaluate   at (u,v) = ( 1, 5) for the function w(x, y) = xy -   ; x = u - v, y = uv.

Accepted Answer

A)  -4 
B)  1 
C)  -65 
D)  6 
A)  -4 
B)  1 
C)  -65 
D)  6

Question 7

Sketch the surface z = f(x,y).
-f(x, y) = 1 - x - 2y

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

Use polar coordinates to find the limit of the function as (x, y) approaches (0, 0).
-f(x, y) =

Accepted Answer

A)  1 
B)  2 
C)  0 
D)  No limit 
A)  1 
B)  2 
C)  0 
D)  No limit

Question 10

Find the derivative of the function at the given point in the direction of A.
-

Accepted Answer

A)  - 708,588 
B)  - 885,735 
C)  - 354,294 
D)  - 531,441 
A)  - 708,588 
B)  - 885,735 
C)  - 354,294 
D)  - 531,441

Question 11

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

Accepted Answer

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

Question 12

Solve the problem. 
-Find the least squares line through the points   and

Accepted Answer

A)  y = -4x + 22 
B)  y = -16x + 2 
C)  y = -4x + 2 
D)  y = -16x + 22 
A)  y = -4x + 22 
B)  y = -16x + 2 
C)  y = -4x + 2 
D)  y = -16x + 22

Question 13

Find the domain and range and describe the level curves for the function f(x,y).
-f(x, y) = ln ( 7x + 10y)

Accepted Answer

A)  Domain: all points in the xy-plane; range: all real numbers; level curves: lines  7x + 10y = c 
B)   Domain: all points in the xy-plane satisfying   7x +  10y > 0; range: all real numbers; level curves: lines  7x + 10y = c 
C)   Domain: all points in the xy-plane satisfying   7x +  10y ≥ 0; range: all real numbers; level curves: lines  7x + 10y = c 
D)   Domain: all points in the xy-plane satisfying   7x +  10y > 0; range: real numbers  z ≥ 0; level curves: 7x + 10y = c lines 
A)  Domain: all points in the xy-plane; range: all real numbers; level curves: lines  7x + 10y = c 
B)   Domain: all points in the xy-plane satisfying   7x +  10y > 0; range: all real numbers; level curves: lines  7x + 10y = c 
C)   Domain: all points in the xy-plane satisfying   7x +  10y ≥ 0; range: all real numbers; level curves: lines  7x + 10y = c 
D)   Domain: all points in the xy-plane satisfying   7x +  10y > 0; range: real numbers  z ≥ 0; level curves: 7x + 10y = c lines

Question 14

Solve the problem.
-Find the derivative of the function   at the point   in the direction in which the function decreases most rapidly.

Accepted Answer

A)  - 3/5   
B)  - 2/5   
C)  - 3/5   
D)  - 2/5   
A)  - 3/5   
B)  - 2/5   
C)  - 3/5   
D)  - 2/5

Question 15

Solve the problem.
-Find the derivative of the function   at the point   in the direction in which the function increases most rapidly.

Accepted Answer

A)  8 
B)  27 
C)  9 
D)  18 
A)  8 
B)  27 
C)  9 
D)  18

Question 16

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

Accepted Answer

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

Question 17

Find all the second order partial derivatives of the given function.
-f(x, y) = x   + y   + 5

Accepted Answer

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

Question 18

Find the domain and range and describe the level curves for the function f(x,y).
-f(x, y) = 3   - 5

Accepted Answer

A)   Domain: all points in the xy-plane; range: all real numbers; level curves: hyperbolas    
B)   Domain: all points in the xy-plane; range: real numbers z ≥ 0; level curves: ellipses    
C)   Domain: all points in the xy-plane; range: all real numbers; level curves: ellipses     
D)   Domain: all points in the first quadrant of the xy-plane; range: all real numbers; level curves: hyperbolas    
A)   Domain: all points in the xy-plane; range: all real numbers; level curves: hyperbolas    
B)   Domain: all points in the xy-plane; range: real numbers z ≥ 0; level curves: ellipses    
C)   Domain: all points in the xy-plane; range: all real numbers; level curves: ellipses     
D)   Domain: all points in the first quadrant of the xy-plane; range: all real numbers; level curves: hyperbolas

Question 19

Find all the first order partial derivatives for the following function.       
-f(x, y) = 10x - 3   - 6

Accepted Answer

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

Question 20

Write a chain rule formula for the following derivative.
-  for w = f(x, y, z); x = g(r, s, t), y = h(r, s, t), z = k(r, s, t)

Accepted Answer

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

Solve the problem. -Find the equation for the tangent plane to the surface at the point

Solve the problem. -Evaluate at t = 9 for the function w(x, y, z) = ; x = t, y = t, z = .

Solve the problem. -Evaluate at (u, v) = ( 5, 3) for the function w(x, y, z) = xz + yz - ; x = uv, y = uv, z = u.

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

Solve the problem. -Find the distance from the point to the plane

Solve the problem. -Evaluate at (u,v) = ( 1, 5) for the function w(x, y) = xy - ; x = u - v, y = uv.

Sketch the surface z = f(x,y). -f(x, y) = 1 - x - 2y

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

Use polar coordinates to find the limit of the function as (x, y) approaches (0, 0). -f(x, y) =

Find the derivative of the function at the given point in the direction of A. -

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

Solve the problem. -Find the least squares line through the points and

Find the domain and range and describe the level curves for the function f(x,y). -f(x, y) = ln ( 7x + 10y)

Solve the problem. -Find the derivative of the function at the point in the direction in which the function decreases most rapidly.

Solve the problem. -Find the derivative of the function at the point in the direction in which the function increases most rapidly.

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

Find all the second order partial derivatives of the given function. -f(x, y) = x + y + 5

Find the domain and range and describe the level curves for the function f(x,y). -f(x, y) = 3 - 5

Find all the first order partial derivatives for the following function. -f(x, y) = 10x - 3 - 6

Write a chain rule formula for the following derivative. - for w = f(x, y, z); x = g(r, s, t), y = h(r, s, t), z = k(r, s, t)

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