Question 1

Find the partial derivative.
-Find

Accepted Answer

A)  8x - 11y 
B)  -11x - 12y 
C)    
D)    
A)  8x - 11y 
B)  -11x - 12y 
C)    
D)

Question 2

Provide an appropriate response.
-Use Lagrange multipliers to maximize f(x, y) = 5xy subject to x + y = - 6.

Accepted Answer

A)  max f(x, y) = f(-3, -3) = 45 
B)  max f(x, y) = f(-3, 3) = -45 
C)  max f(x, y) = f(3, -3) = -45 
D)  max f(x, y) = f(3, 3) = 45 
A)  max f(x, y) = f(-3, -3) = 45 
B)  max f(x, y) = f(-3, 3) = -45 
C)  max f(x, y) = f(3, -3) = -45 
D)  max f(x, y) = f(3, 3) = 45

Question 3

Provide an appropriate response.
-Find the local extrema for

Accepted Answer

A)  f(0, 0) = 0 is a minimum 
B)  f(0, 2) = 4 is a maximum 
C)  f(2, 0) = -16 is a minimum 
D)  f(0, 0) = 0 is a maximum 
A)  f(0, 0) = 0 is a minimum 
B)  f(0, 2) = 4 is a maximum 
C)  f(2, 0) = -16 is a minimum 
D)  f(0, 0) = 0 is a maximum

Question 4

Solve the problem.
-The table lists the high school grade-point averages of six students and their college grade-point averages after one year of college.   Use the least-squares line to estimate the college GPA for a student with a high school GPA of 3.5.

Accepted Answer

A)  about 2.6 
B)  about 3.0 
C)  about 3.2 
D)  about 2.8 
A)  about 2.6 
B)  about 3.0 
C)  about 3.2 
D)  about 2.8

Question 5

Solve the problem.
-The volume of a flower pot is given by   where   is the major radius and   is the minor radius and h is the height of the pot (see figure below).   If the dimensions of the pot are   = 5 inches,   = 3 inches and h = 6 inches, find the volume of potting soil
Required to fill the pot to the top. Round to the nearest cubic inch.

Accepted Answer

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

Question 6

Provide an appropriate response.
-Use Lagrange multiplier to maximize f(x, y, z) = xy + z subject to

Accepted Answer

A)  f(1, 1, 1) = 1 
B)  f(1, 1, 0) = 1 
C)  f(0, 1, 0) = 1 
D)  f(0, 0, 1) = 1 
A)  f(1, 1, 1) = 1 
B)  f(1, 1, 0) = 1 
C)  f(0, 1, 0) = 1 
D)  f(0, 0, 1) = 1

Question 7

Provide an appropriate response.
-Find the local extrema for

Accepted Answer

A)  (2, 1) = -8 is a minimum 
B)  (- 2, - 1) = 9 is a maximum 
C)  (- 2, 1) = 9 is a minimum 
D)  (2, 1) = -8 is a maximum 
A)  (2, 1) = -8 is a minimum 
B)  (- 2, - 1) = 9 is a maximum 
C)  (- 2, 1) = 9 is a minimum 
D)  (2, 1) = -8 is a maximum

Question 8

Provide an appropriate response.
-Find the double integral over the rectangular region R with the given boundaries.

Accepted Answer

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

Question 9

Find the partial derivative.
-For

Accepted Answer

A)  12 
B)  36 
C)  24 
D)  -12 
A)  12 
B)  36 
C)  24 
D)  -12

Question 10

Choose the surface that the function describes.
-f(x, y) = 5

Accepted Answer

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

Question 11

Provide an appropriate response.
-Find

Accepted Answer

A)  -28 
B)    
C)  -14 
D)    
A)  -28 
B)    
C)  -14 
D)

Question 12

Evaluate the integral.
-Evaluate the integral with the order reversed.

Accepted Answer

A)    
B)    
C)  4 
D)    
A)    
B)    
C)  4 
D)

Question 13

Provide an appropriate response.
-Evaluate

Accepted Answer

A)  -12 
B)  15 
C)  12 
D)  24 
A)  -12 
B)  15 
C)  12 
D)  24

Question 14

Solve the problem.
-The market research department for a drug store chain arrived at the demand table below, where y is the number of bottles of multivitamins purchased per month (in thousands) at x dollars per bottle.   I) Find a demand equation using the method of least squares.
II) If each bottle of multivitamins costs the drug store chain $4, how should it be priced to achieve a maximum monthly
Profit? [Hint: Use the result from I) with C = 4y, R = xy, and P = R - C.]

Accepted Answer

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

Question 15

Solve the problem.
-Poiseuille's law states that the resistance, R, for blood in a blood vessel varies directly as the length of the vessel, L, and inversely as the fourth power of its diameter, d. This can be written as an equation   where
K is a constant. Find R(5, 0.3). Round your answer to the nearest whole number.

Accepted Answer

A)  about 61.7k 
B)  about 617k 
C)  about 16.67k 
D)  about 630k 
A)  about 61.7k 
B)  about 617k 
C)  about 16.67k 
D)  about 630k

Question 16

Provide an appropriate response.
-Find fxy for the function

Accepted Answer

The answer of Provide an appropriate response.
-Find fxy for the...

Question 17

Solve the problem.
-The productivity of a major manufacturer of microwave ovens is given approximately by the Cobb-Douglas production function   with the utilization of x units of labor and y units of capital. If the
Company is currently utilizing 4500 units of labor and 2000 units of capital, find the marginal productivity of
Labor to the nearest unit.

Accepted Answer

A)  129 units 
B)  2 units 
C)  217 units 
D)  32 units 
A)  129 units 
B)  2 units 
C)  217 units 
D)  32 units

Question 18

Provide an appropriate response.
-Find critical points for

Accepted Answer

A)  (4, -3) 
B)  (-4, 3) 
C)  (4, 3) 
D)  (-4, -3) 
A)  (4, -3) 
B)  (-4, 3) 
C)  (4, 3) 
D)  (-4, -3)

Question 19

Find the partial derivative.
-Let z =

Accepted Answer

A)    
B)  -12x - 18y 
C)  10x - 12y 
D)    
A)    
B)  -12x - 18y 
C)  10x - 12y 
D)

Question 20

Find the value.
-Let   Find f(4, -7).

Accepted Answer

A)  198 
B)  (4, -7) is not in the domain of f. 
C)  -24 
D)  -119 
A)  198 
B)  (4, -7) is not in the domain of f. 
C)  -24 
D)  -119

Find the partial derivative. -Find

Provide an appropriate response. -Use Lagrange multipliers to maximize f(x, y) = 5xy subject to x + y = - 6.

Provide an appropriate response. -Find the local extrema for

Solve the problem. -The table lists the high school grade-point averages of six students and their college grade-point averages after one year of college. Use the least-squares line to estimate the college GPA for a student with a high school GPA of 3.5.

Provide an appropriate response. -Use Lagrange multiplier to maximize f(x, y, z) = xy + z subject to

Provide an appropriate response. -Find the local extrema for

Provide an appropriate response. -Find the double integral over the rectangular region R with the given boundaries.

Find the partial derivative. -For

Choose the surface that the function describes. -f(x, y) = 5

Provide an appropriate response. -Find

Evaluate the integral. -Evaluate the integral with the order reversed.

Provide an appropriate response. -Evaluate

Provide an appropriate response. -Find fxy for the function

Provide an appropriate response. -Find critical points for

Find the partial derivative. -Let z =

Find the value. -Let Find f(4, -7).

Functions and Graphs

Limits and the Derivative

Additional Derivative Topics

Graphing and Optimization

Integration

Additional Integration Topics

Trigonometric Functions

Differential Equations

Taylor Polynomials and Infinite Series

Probability and Calculus

Basic Algebra Review

Special Topics

Filters

Exam 7: Multivariable Calculus

Find the partial derivative. -Find

Provide an appropriate response. -Use Lagrange multipliers to maximize f(x, y) = 5xy subject to x + y = - 6.

Provide an appropriate response. -Find the local extrema for

Solve the problem. -The table lists the high school grade-point averages of six students and their college grade-point averages after one year of college. Use the least-squares line to estimate the college GPA for a student with a high school GPA of 3.5.

Provide an appropriate response. -Use Lagrange multiplier to maximize f(x, y, z) = xy + z subject to

Provide an appropriate response. -Find the local extrema for

Provide an appropriate response. -Find the double integral over the rectangular region R with the given boundaries.

Find the partial derivative. -For

Choose the surface that the function describes. -f(x, y) = 5

Provide an appropriate response. -Find

Evaluate the integral. -Evaluate the integral with the order reversed.

Provide an appropriate response. -Evaluate

Provide an appropriate response. -Find fxy for the function

Provide an appropriate response. -Find critical points for

Find the partial derivative. -Let z =

Find the value. -Let Find f(4, -7).

Functions and Graphs

Limits and the Derivative

Additional Derivative Topics

Graphing and Optimization

Integration

Additional Integration Topics

Trigonometric Functions

Differential Equations

Taylor Polynomials and Infinite Series

Probability and Calculus

Basic Algebra Review

Special Topics

Filters