Question 1

Find the sum of the squared errors for the linear model   and the quadratic model   using the given points. ​   ​

Accepted Answer

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

Question 2

Evaluate the function at the given values of the independent variables. ​   ​

Accepted Answer

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

Question 3

Describe the trace of the surface given by the function below   in the xz-plane. ​

Accepted Answer

A)  circle 
B)  parabola 
C)  line 
D)  ellipse (not circle) 
E)  hyperbola 
A)  circle 
B)  parabola 
C)  line 
D)  ellipse (not circle) 
E)  hyperbola

Question 4

A manufacturer estimates the Cobb-Douglas production function to be given by ​   ​
Estimate the production levels when   and   ​

Accepted Answer

A)  135,540 units 
B)  122,560 units 
C)  131,601 units 
D)  145,330 units 
E)  112,745 units 
A)  135,540 units 
B)  122,560 units 
C)  131,601 units 
D)  145,330 units 
E)  112,745 units

Question 5

Evaluate the function   at   ​

Accepted Answer

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

Question 6

Use Lagrange multipliers to find the given extremum.In each case,assume that x,y​,and z are positive. ​
Maximize   Constraints   ​

Accepted Answer

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

Question 7

Find the intercepts of the plane given by   ​

Accepted Answer

A)  ​​The x​-intercept is   The z-intercept is   ​ 
B)  ​​​​The x​-intercept is   The z-intercept is   ​​ 
C)  ​​​The x​-intercept is   The z-intercept is   ​​ 
D)  ​​The x​-intercept is   The z-intercept is   ​ 
E)  ​The x​-intercept is   The z-intercept is   ​ 
A)  ​​The x​-intercept is   The z-intercept is   ​ 
B)  ​​​​The x​-intercept is   The z-intercept is   ​​ 
C)  ​​​The x​-intercept is   The z-intercept is   ​​ 
D)  ​​The x​-intercept is   The z-intercept is   ​ 
E)  ​The x​-intercept is   The z-intercept is   ​

Question 8

Use Lagrange multipliers to minimize the function   subject to the following constraint. ​   ​
Assume that x,y,and z are positive.
​

Accepted Answer

A)  ​4 
B)  ​12 
C)  ​8 
D)  ​24 
E)  ​36 
A)  ​4 
B)  ​12 
C)  ​8 
D)  ​24 
E)  ​36

Question 9

Find the domain and range of the function. ​   ​

Accepted Answer

A)  Domain: all point   such that  
Range:   
B)  Domain: all point   such that  
Range:   
C)  Domain: all point   such that  
Range:   
D)  Domain: all point   such that  
Range:   
E)  Domain: all point   such that  
Range:   
A)  Domain: all point   such that  
Range:   
B)  Domain: all point   such that  
Range:   
C)  Domain: all point   such that  
Range:   
D)  Domain: all point   such that  
Range:   
E)  Domain: all point   such that  
Range:

Question 10

Find the intercepts of the plane given by   ​

Accepted Answer

A)  ​The x-intercept is   The y-intercept is   The z-intercept is   ​ 
B)  ​​The x-intercept is   The y-intercept is   The z-intercept is   ​​​ 
C)  ​​​The x-intercept is   The y-intercept is   The z-intercept is   ​​​ 
D)  ​​The x-intercept is   The y-intercept is   ​
The z-intercept is   ​​ 
E)  ​​The x-intercept is   The y-intercept is   The z-intercept is   ​​ 
A)  ​The x-intercept is   The y-intercept is   The z-intercept is   ​ 
B)  ​​The x-intercept is   The y-intercept is   The z-intercept is   ​​​ 
C)  ​​​The x-intercept is   The y-intercept is   The z-intercept is   ​​​ 
D)  ​​The x-intercept is   The y-intercept is   ​
The z-intercept is   ​​ 
E)  ​​The x-intercept is   The y-intercept is   The z-intercept is   ​​

Question 11

Sketch the trace of the intersection of plane   with the sphere: ​   ​

Accepted Answer

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

Question 12

Examine the function   for relative extrema. ​

Accepted Answer

A)  saddle point at   
B)  ​relative minimum at   
C)  ​saddle point at   
D)  ​relative maximum at   
E)  ​saddle point at   
A)  saddle point at   
B)  ​relative minimum at   
C)  ​saddle point at   
D)  ​relative maximum at   
E)  ​saddle point at

Question 13

An agronomist used four test plots to determine the relationship between the wheat yield y (in bushels per acre)and the amount of fertilizer x (in pounds per acre).The results are shown in the table. ​
 
​(I)Use the regression capabilities of a graphing utility or a spreadsheet to find the least squares regression line for the data.
​(II)Estimate the yield for a fertilizer application of 160 pounds per acre.
​

Accepted Answer

A)  (I)   ; (II) 39.10 
B)  (I)   ; (II) 45.90 
C)  (I)   ; (II) 44.18 
D)  (I)   ; (II) 42.32 
E)  (I)   ; (II)54.94 
A)  (I)   ; (II) 39.10 
B)  (I)   ; (II) 45.90 
C)  (I)   ; (II) 44.18 
D)  (I)   ; (II) 42.32 
E)  (I)   ; (II)54.94

Question 14

Sketch the trace of the intersection of plane   with the sphere: ​   ​

Accepted Answer

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

Question 15

Find the first partial derivatives with respect to x,y,and z. ​   ​
​

Accepted Answer

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

Question 16

Use a double integral to find the area of the region bounded by the graphs of   ​

Accepted Answer

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

Question 17

Examine the function given below for relative extrema and saddle points. ​   ​

Accepted Answer

A)  The function has a relative minimum at   
B)  The function has a relative maximum at   
C)  The function has a saddle point at   
D)  The function has a saddle point at   
E)  The function has a relative maximum at   
A)  The function has a relative minimum at   
B)  The function has a relative maximum at   
C)  The function has a saddle point at   
D)  The function has a saddle point at   
E)  The function has a relative maximum at

Question 18

Sketch the region R whose area is given by the following double integral. ​   ​

Accepted Answer

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

Question 19

Find the center and radius of the sphere. ​   ​

Accepted Answer

A)  Center:  
Radius:   
B)  Center:  
Radius:   
C)  Center:  
Radius:   
D)  Center:  
​Radius:   
E)  Center:  
Radius:   
A)  Center:  
Radius:   
B)  Center:  
Radius:   
C)  Center:  
Radius:   
D)  Center:  
​Radius:   
E)  Center:  
Radius:

Question 20

Examine the function given below for relative extrema and saddle points. ​   ​

Accepted Answer

A)  The function has a saddle point at   
B)  The function has a relative maximum at   
C)  The function has a relative minimum at   
D)  The function has a saddle point at   
E)  The function has a relative maximum at   
A)  The function has a saddle point at   
B)  The function has a relative maximum at   
C)  The function has a relative minimum at   
D)  The function has a saddle point at   
E)  The function has a relative maximum at

Find the sum of the squared errors for the linear model and the quadratic model using the given points.

Evaluate the function at the given values of the independent variables.

Describe the trace of the surface given by the function below in the xz-plane.

A manufacturer estimates the Cobb-Douglas production function to be given by Estimate the production levels when and

Evaluate the function at

Use Lagrange multipliers to find the given extremum.In each case,assume that x,y,and z are positive. Maximize Constraints

Find the intercepts of the plane given by

Use Lagrange multipliers to minimize the function subject to the following constraint. Assume that x,y,and z are positive.

Find the domain and range of the function.

Find the intercepts of the plane given by

Sketch the trace of the intersection of plane with the sphere:

Examine the function for relative extrema.

Sketch the trace of the intersection of plane with the sphere:

Find the first partial derivatives with respect to x,y,and z.

Use a double integral to find the area of the region bounded by the graphs of

Examine the function given below for relative extrema and saddle points.

Sketch the region R whose area is given by the following double integral.

Find the center and radius of the sphere.

Examine the function given below for relative extrema and saddle points.

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

Exam 7: Functions of Several Variables

Find the sum of the squared errors for the linear model and the quadratic model using the given points. ​ ​

Evaluate the function at the given values of the independent variables. ​ ​

Describe the trace of the surface given by the function below in the xz-plane. ​

A manufacturer estimates the Cobb-Douglas production function to be given by ​ ​ Estimate the production levels when and ​

Evaluate the function at ​

Use Lagrange multipliers to find the given extremum.In each case,assume that x,y​,and z are positive. ​ Maximize Constraints ​

Find the intercepts of the plane given by ​

Use Lagrange multipliers to minimize the function subject to the following constraint. ​ ​ Assume that x,y,and z are positive. ​

Find the domain and range of the function. ​ ​

Find the intercepts of the plane given by ​

Sketch the trace of the intersection of plane with the sphere: ​ ​

Examine the function for relative extrema. ​

Sketch the trace of the intersection of plane with the sphere: ​ ​

Find the first partial derivatives with respect to x,y,and z. ​ ​ ​

Use a double integral to find the area of the region bounded by the graphs of ​

Examine the function given below for relative extrema and saddle points. ​ ​

Sketch the region R whose area is given by the following double integral. ​ ​

Find the center and radius of the sphere. ​ ​

Examine the function given below for relative extrema and saddle points. ​ ​

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Trigonometric Functions

Probability and Calculus

Series and Taylor Polynomials

Differential Equations

Filters

Find the sum of the squared errors for the linear model and the quadratic model using the given points.

Evaluate the function at the given values of the independent variables.

Describe the trace of the surface given by the function below in the xz-plane.

A manufacturer estimates the Cobb-Douglas production function to be given by Estimate the production levels when and

Evaluate the function at

Use Lagrange multipliers to find the given extremum.In each case,assume that x,y,and z are positive. Maximize Constraints

Find the intercepts of the plane given by

Use Lagrange multipliers to minimize the function subject to the following constraint. Assume that x,y,and z are positive.

Find the domain and range of the function.

Find the intercepts of the plane given by

Sketch the trace of the intersection of plane with the sphere:

Examine the function for relative extrema.

Sketch the trace of the intersection of plane with the sphere:

Find the first partial derivatives with respect to x,y,and z.

Use a double integral to find the area of the region bounded by the graphs of

Examine the function given below for relative extrema and saddle points.

Sketch the region R whose area is given by the following double integral.

Find the center and radius of the sphere.

Examine the function given below for relative extrema and saddle points.